Born March 14, 1922, at Mexia, Texas. He learned to play the piano at five years of age and studied at the Detroit Conservatory and at Pepperdine College in Los Angeles, California (his uncle was the college's first president). He began his career as a concert pianist but later joined Mel Tormé's "Meltones" in 1945. Baxter conducted a number of radio shows including "The Bob Hope Show". His recording of "The Poor People of Paris" in March 1956 was a #1 hit and sold more single copies than any other recording during that decade (the song got that title by mistake. Originally titled "The Ballad of Poor John" when it was popularized in France, a Capitol Records representative cabled the title to the US; the cable used the word "gens", meaning "people", instead of "jean"). Another major hit was "April in Portugal", which was based on a song by Raúl Ferrão. It was originally entitled "Coimbra" (after a city in Portugal) and later introduced in the US as the whispering serenade. But Jimmy Kennedy wrote a new set of lyrics in 1952 for it and it became a huge hit for Baxter\, who also wrote the scores for over 120 motion pictures.
He died of heart and kidney problems on January 15, 1996.