Dresser was born in Chicago, Illinois, but mostly grew up in West Texas. Here he lost an eye to barbed wire as a boy, and thus had to wear an eye patch for the rest of his life. At the age of 14, he ran away from home and enlisted in the U.S. 5th Cavalry Regiment at Fort Bliss, Texas, followed by a year of Border Patrol duty on the Rio Grande. After his service, he returned to Texas to finish high school. In search of adventure, Dresser traveled throughout the Southwest working at various odd jobs, including that of muleskinner, farm hand, deckhand on a freighter in the Gulf of Mexico, laborer in the California oilfields, etc. Eventually, he went to Tri-State College of Engineer, where he received a certificate in civil engineering. Back in Texas, he worked as an engineer and surveyor for several years before turning to writing in 1927.

After his first marriage (to Kathleen Rollins, who had two daughters from a previous marriage), Dresser was married to mystery writer Helen McCloy from 1946 to 1961; they had a daughter named Chloe. As partners, they formed a literary agency called Halliday and McCloy. Dresser also established a publishing company Torquil Publishing Company, which published his books as well as those of other authors, from 1953 to 1965. In 1961, he married Mary Savage, also a writer; their son, Halliday, was born in 1965.

The first Shayne novel was rejected by 21 publishers before being accepted by Henry Holt & Co. in 1939. The Shayne series went on to be highly successful, reprinted in many editions and translated into French, Spanish, Italian, German, Swedish, Japanese and Hebrew. A radio series based on the Shayne character was heard during the 1940s. Twelve motion pictures were made, seven of them featuring Lloyd Nolan as Shayne. Five of the Nolan films, which were produced by 20th Century Fox, have been released on DVD: Michael Shayne, Private Detective; Sleepers West; Dressed to Kill; Blue, White and Perfect; and The Man Who Wouldn't Die. After the Fox series ended, five more Shayne films were made by PRC which featured Hugh Beaumont as the detective. There was also a TV series in 1960, starring Richard Denning. The 2005 film Kiss Kiss Bang Bang is based partly on Halliday's novel Bodies Are Where You Find Them.

Dresser was a founding member of the Mystery Writers of America, and in 1954 he and McCloy were given Edgar Awards for their critical writings on the genre.

He lived in Santa Barbara, California, until his death at the age of 72.