Burns was born May 18, 1935 in Baltimore, Maryland, United States. He attended the University of Oregon between 1953 and 1957.

He is a former writer for The Bullwinkle Show. Burns also produced three other television shows, Cutters (1993), The Duck Factory (1984) and (with Chris Hayward), the unaired version of the 1965 pilot episode of The Smothers Brothers Show. Before breaking into television and film, Burns started in animation, working for Jay Ward and collaborating and animating Rocky and Bullwinkle and George of the Jungle. Burns also created the Cap'n Crunch character for Quaker Oats.

After his stint writing for Jay Ward, Burns formed a partnership with Chris Hayward and they created the series The Munsters and were later hired by producer Leonard Stern as story editors for the CBS series He & She, for which they won an Emmy award for comedy writing. The last project between Hayward and Burns would be as story editors for the sitcom, Get Smart.

In 1969, Burns began a partnership with James L. Brooks after being impressed with the television pilot for Brooks's show Room 222. Burns joined the Room 222 writing staff and later produced the series.

After Room 222, television executive Grant Tinker hired Brooks and Burns to develop a television series for CBS starring Mary Tyler Moore. In 1970, The Mary Tyler Moore Show premiered and became a critically acclaimed series, spawning spin-off series such as Lou Grant and Rhoda. Burns also wrote and produced three television series; F.M., Eisenhower and Lutz and Cutters.

Burns has also done screenwriting for movies. Most notably, A Little Romance for which he was nominated for an Academy Award for Writing Adapted Screenplay. He also wrote the screenplays The Early Days, Just the Way You Are and wrote and directed Just Between Friends.