He was born Armando Greco in Philadelphia, Pennsylvania. Greco began playing piano at the age of four. His first professional work was playing with Benny Goodman's band. Most of Greco's work has been in the jazz and pop genres. He has recorded songs such as Oh Look A-There, Ain't She Pretty, "The Lady is a Tramp", "Up, Up and Away" and "Around the World", and has released about 72 albums and 100 singles. Greco has had an active concert career playing in symphony halls, theatres, nightclubs, and Las Vegas showrooms. In the 1960s he made appearances with the Rat Pack. Greco played the nightclub singer Lucky in the 1969 film The Girl Who Knew Too Much. In 1967, Greco starred in the summer replacement television series Away We Go with drummer Buddy Rich and comedian George Carlin.
Greco has recorded albums for the Columbia/Epic and Reprise record labels, and other minor labels. His most popular albums were On Stage and Buddy's Back in Town, both with Columbia. His most successful single was "The Lady is a Tramp", which sold over one million copies and was awarded a gold disc. Greco recorded an album entitled Movin' On which included his version of the Marvin Gaye standard "What's Going On". Greco recorded sporadically after this album, but he continued performing live shows, and has performed in most of the top nightclubs in the world. His last nationally charted record was "From Atlanta to Goodbye", on the Scepterlabel, which made Billboard's Easy Listening Top 40 in 1969.
Greco performed the vocal theme to the 1972 film Something to Hide, How Can We Run Away (Theme From Something to Hide) that was composed by Roy Budd (uncredited on the film).