Parish was born Michael Hyman Pashelinsky to a Jewish family in Lithuania. His family emigrated to the United States, arriving on February 3, 1901 on the SS Dresden when he was less than a year old. They settled first in Louisiana where his paternal grandmother had relatives, but later moved to New York City.
By the late 1920s Parish was a well-regarded Tin Pan Alley lyricist in New York City.
His best-known works include the lyrics to songs such as "Star Dust," "Sweet Lorraine," "Deep Purple," "Stars Fell on Alabama," "Sophisticated Lady," the translation to English lyrics of "Volare," "Moonlight Serenade," "Mr. Ghost Goes to Town," "Sleigh Ride," "One Morning in May," and "Louisiana Fairy Tale," which was the first theme song used in the PBS Production of This Old House.
Besides providing the lyrics to Hoagy Carmichael's "Star Dust," the two collaborated on standards such as "Riverboat Shuffle" and "One Morning in May."
In 1949, Parish added lyrics to bandleader Al Goodman's tune, "The Allen Stroll," which was played as radio comedian Fred Allen took a stroll down "Allen's Alley", a featured segment of Allen's weekly show. The new song, "Carousel of Love," premiered on The Fred Allen Show on April 4, 1949. It was sung by the DeMarco Sisters and played by Al Goodman and his Orchestra.
In 1951, he wrote the English lyrics of the French song Maître Pierre which was written in 1948 by Henri Betti (music) and Jacques Plante (lyrics). The title song became The Windmill Song and the song was recorded by The Andrews Sisters with Gordon Jenkins and his Orchestra.
In 1987, a revue titled Stardust was staged on Broadway featuring Parish's lyrics. It ran for 101 performances and was revived in 1999. In an interview at the time Parish claimed to have also written the lyrics to the Duke Ellington standard "Mood Indigo" though they were credited to Irving Mills. He remained "somewhat rueful, though no longer bitter" about it.
Parish's grandnephew was the Grateful Dead roadie Steve Parish, who described Parish's meeting with Jerry Garcia in his autobiography, Home Before Day Light.
In 1972, he was inducted into the Songwriters Hall of Fame.
Parish died in 1993 in Manhattan at the age of 92. He was buried in Beth David Cemetery in Elmont, New York.Continental Varieties (1935) - revue - featured lyricist
Lew Leslie's Blackbirds of 1939 (1939) - revue - performer
Earl Carroll's Vanities of 1940 (1940) - revue - featured lyricist
Bubbling Brown Sugar (1976) - revue - featured lyricist
Sophisticated Ladies (1981) - featured lyricist for "Sophisticated Lady"
Stardust (1987) - revue - lyricist