The cause of Adler's death Thursday at his Southampton home was not reported.
Along with fellow composer and lyricist Jerry Ross, Adler wrote songs in the 1950s for the two musicals, which each ran for more than 1,000 performances.
Songs such as "Hey There" and "Hernando's Hideaway" from "The Pajama Game" and "Heart" and "Whatever Lola Wants (Lola Gets)" from "Damn Yankees" quickly became hits after their 1954 and 1955 releases respectively, The New York Times reported Saturday.
After the abrupt death of Ross in 1955, Adler mostly worked as a producer and wrote advertising jingles, including "Let Hertz Put You in the Driver's Seat." He was also responsible for producing the 1962 Madison Square Garden fundraiser that featured Marilyn Monroe singing "Happy Birthday, Mr. President" to President John F. Kennedy, the Times said.