Born in Pennsylvania, United States in 1956, Meyer grew up in Tucson, Arizona. He is the eldest of eight children in a Roman Catholic family of German ancestry. His parents both worked in the real estate business. Meyer has made jokes about his somewhat unhappy childhood, stating that one common argument in his household was "which family member ruined a holiday", while his sister noted Meyer was frequently blamed for the family's problems. Due to its size, family activities were limited so Meyer watched lots of television and read Mad magazine. He was an Eagle Scout and an altar boy and wrote for the student newspaper.

Meyer attended Harvard University where he served as president of the Harvard Lampoon. The fact that people took humor "very seriously" at the Lampoon "changed [Meyer's] life". In 1977, he and several other Lampoon staffers wrote The Harvard Lampoon Big Book of College Life (ISBN 0385134460), a volume commissioned by Doubleday. Aside from the Lampoon, his grades at Harvard were average and he suffered several bouts of depression. He graduated in 1978 with a degree in biochemistry and was accepted into medical school, but decided not to enroll.

Meyer commented on his Roman Catholic upbringing in a 2000 New Yorker profile:

"People talk about how horrible it is to be brought up Catholic, and it's all true. The main thing was that there was no sense of proportion. I would chew a piece of gum at school, and the nun would say, 'Jesus is very angry with you about that,' and on the wall behind her would be a dying, bleeding guy on a cross. That's a horrifying image to throw at a little kid. You really could almost think that your talking in line, say, was on a par with killing Jesus."

After college, Meyer moved to Denver, Colorado, planning to "scientifically" win a fortune through dog racing. However, he ran out of money after two weeks. He then worked in a variety of jobs including as a substitute teacher, a laboratory research assistant and a salesman in a clothing store and also won $2000 on the game show Jeopardy!. In 1981, he was given a job by David Letterman as a member of the writing staff on Letterman's new late night show and moved to New York, having been recommended by fellow Lampoon writers Tom Gammill and Max Pross. Letterman noted: "Everything in his submission, down to the last little detail, was so beautifully honed." Meyer wrote several recurring gags for the show, including "Crushing Things With A Steamroller".

Two seasons later, Meyer left to write for The New Show; with that show's cancellation after two months he moved on to Not Necessarily the News and then Saturday Night Live. Meyer's work was not well-regarded among the SNL writers and producers. He said: "My stuff wasn't very popular at Saturday Night. It was regarded as really fringey, and a lot of times my sketches would get cut. Sometimes they would get cut after dress rehearsal, and I would have the horrible experience of looking out and seeing a painter carefully touching up my set and getting it all ready to be smashed to pieces and sent to a landfill in Brooklyn. It was just a mismatch, although I didn't realize it at the time." He left the show in 1987.

Meyer moved to Boulder, Colorado because he "just wanted to get as far from the New York environment as [he] could." There, he wrote a film script for Letterman; the project was dropped due to the success of Letterman's show, although several of its jokes were later used in The Simpsons when no other ideas could be found. He founded the humor zine Army Man; he wrote the eight-page first issue almost wholly by himself, publishing just 200 copies which he gave to his friends. Meyer had been disappointed by the decline of the National Lampoon and felt that there was no longer a magazine which has the sole purpose of being funny. By starting Army Man he "tried to make something that had no agenda other than to make you laugh." He claimed that "[he] didn't know what [he] was doing," and reprinted material without obtaining permission, including a review of Cannonball Run II. He added: "I like to think that Army Man was somewhere between a real publication and a very irresponsible, lawbreaking zine." Army Man gained a strong following and was listed on Rolling Stone's "Hot List" in 1989. Meyer noted: "The only rule was that the stuff had to be funny and pretty short. To me, the quintessential Army Man joke was one of John Swartzwelder's: 'They can kill the Kennedys. Why can't they make a cup of coffee that tastes good?' It's a horrifying idea juxtaposed with something really banal-and yet there's a kind of logic to it. It's illuminating because it's kind of how Americans see things: Life's a big jumble, but somehow it leads to something I can consume. I love that." Meyer suspended publication with the third issue, after offers to take the magazine national made him fear that it would lose its best qualities. According to The Believer: "In comedy circles, [Army Man has] taken on almost mythological proportions."One reader was Sam Simon, a producer of the animated sitcom The Simpsons. In 1989, Simon hired Meyer as part of the show's writing staff along with Army Man contributors Swartzwelder and Jon Vitti. Meyer often played an active role in the show's extensive group script rewriting sessions in the "rewrite room" a role he performed more than solo script work; indeed he has only been credited for writing twelve episodes. A. O. Scott described him as the "guru" of the room. In the room, according to Mike Reiss, writers would "involuntarily glance at Meyer for approval when they pitch lines of their own". By 1995, Meyer became tired of the show's lengthy writing schedule and decided to leave after the sixth season to work on a film or TV pilot script. He soon returned, however, as a consultant and later as a part of the writing staff again and an executive producer. In 2004 he noted: "It's hard to leave The Simpsons. Every once in a while I get romantic notions that I should be doing something much more subterranean. Something like Army Man, or maybe guerrilla filmmaking." He has attempted several TV projects that were not picked up. He left the show in 2004, and received his final producer credits in season 16. Meyer returned to co-write the 2007 film adaptation of the show, The Simpsons Movie.

Meyer has been publicly credited with "thoroughly shap[ing]...the comedic sensibility" of The Simpsons; in 2000, Mike Scully, the show runner for the series at the time, called him "the best comedy writer in Hollywood." Scully said he was "the main reason" why The Simpsons [was] still so good after all these years." Vitti has said Meyer's "fingerprints are on nearly every script" and he "exerts as much influence on the show as anyone can without being one of the creators," while recounting how "a show that you have the writer's credit for will run, and the next day people will come up to you and tell you how great it was. Then they'll mention their two favorite lines, and both of them will be George's." Bill Oakley noted Meyer has "he's been there since the beginning adding thousands of jokes and plot twists, etc., that everyone considers classic and brilliant.

Meyer has a "deep suspicion of social institutions and tradition in general," which has affected the writing of his own episodes of The Simpsons such as "Homer the Heretic", "Mr. Lisa Goes to Washington" and "Bart vs. Thanksgiving". For his work on The Simpsons, Saturday Night Live and Late Night with David Letterman, Meyer has won and received multiple Primetime Emmy Award nominations, including the award for Outstanding Writing In A Variety Or Music Program in 1989.

Meyer is in a relationship with the writer Maria Semple. They lived together during the 1990s and broke up in 1999, but later got back together. Their child, named Poppy Valentina after Valentina Tereshkova, was born in 2003; being a father gave Meyer a "sense of hopefulness". They live in Seattle. Although raised a Catholic, Meyer hated it and later became agnostic. While working at The Simpsons he became an atheist, taking the advice of fellow writer Mike Reiss. He is a vegetarian, gambler, collector of space program memorabilia, practices yoga and lived in the Santa Monica mountains. Meyer is a fan of the Grateful Dead with Jerry Garcia being the "closest thing in Meyer's life to a spiritual figure." His sister Ann is married to Jon Vitti.

Meyer has a strong interest in the environment and notes that "the only organization that I really care about these days" is Conservation International. In 2005, Meyer cowrote the TBS special Earth To America. The same year, a newly discovered species of moss frogs from Sri Lanka was named Philautus poppiae after Meyer's daughter Poppy, a tribute to he and Semple's dedication to the Global Amphibian Assessment.

In 2006 he wrote a comic, cautionary opinion piece about the environment for BBC News. It begins:

"Are you a hypocrite? Because I certainly am. I'm an animal lover who wears leather shoes; a vegetarian who can't resist smoked salmon. I badger my friends to see the Al Gore movie, but I also fly on fuel-gulping jets. Great clouds of hypocrisy swirl around me. But even a fraud has feelings. And this summer, I'm feeling uneasy; I'm starting to think that our culture's frenzied and mindless assault on the last shreds of nature may not be the wisest course."