Richard Rodgers’ and Lorenz Hart’s 1937 composition The Lady Is a Tramp has been performed by many singers, but the most widely known version is the 1960 recording by Buddy Greco, who has died aged 90. It encapsulated Greco’s jazz-inflected, finger-snapping, wisecracking, dynamic vocal style and went on to sell more than a million copies.

He was born Armando Greco in Philadelphia into a musical Italian-American family. His father was variously a record store owner, a radio show host and an opera critic, and his mother a musician. Armando took up the piano at the age of four in 1930, when he also made his radio debut as a singer. The family could pay for tuition but did not own a piano. He told an interviewer that after each lesson he would “run home and practise on a cut-out of a piano keyboard my father found on the cover of a magazine. I would play this keyboard and actually hear the notes in my head.”

The music heard in the Greco home was classical, but Armando was converted from Enrico Caruso to jazz as soon as he heard a Louis Armstrong record. He turned professional as a teenager and gained a new forename when a bandleader seeking a pianist at the local musicians’ union office asked him: “Buddy, would you like a job?”

Buddy Greco performing The Lady Is a Tramp in 1964

By the late 1940s, Greco was leading his own group, the Three Sharps, and in 1948 he had a hit with a recording of Ooh Look-a There, Ain’t She Pretty, a song first recorded by Fats Waller. The next year the bandleader Benny Goodman offered Greco a job with his orchestra. He was in two minds but followed his father’s advice to “go with Mr Goodman and learn your craft”.

In 1951, Greco left the band to embark on a solo career of nightclub shows, recordings and television appearances (introduced as “Mr Excitement of Song”) that would continue throughout his life. He became the consummate example of what American reviewers called the saloon or lounge singer. He would often extemporise lyrics or call out “talk to me, piano” when embarking on a solo. Greco’s early nightclub act was captured on the 1955 LP Buddy Greco at Mr Kelly’s, recorded at a Chicago nightspot and one of the best of his albums, of which there were more than 60.

The zeal with which he ingratiated himself with audiences delighted some critics and alienated others. Some felt he was beyond parody, although the comedian Jerry Lewis got close with his portrayal of the character Buddy Love in the 1963 film The Nutty Professor.

Greco claimed to have played at least twice in every major club, but his most favoured venues were in Las Vegas and in Britain. For many years he was associated with the Desert Inn in Las Vegas, a city where he caroused with the so-called Rat Pack led by Frank Sinatra and Sammy Davis Jr, who said: “Buddy Greco’s world is a very swinging world.”

Buddy Greco playing Fly Me to the Moon in 1963

He made his first visit to Britain in 1949, performing at the London Palladium with Goodman. He had a home in London for many years and bought a flat in Westcliff-on-Sea, Essex, telling a Big Issue interviewer in 2010 that Southend was “the greatest little city in the world”.

Among the highlights of his British career were the 1963 Royal Variety Performance headlined by the Beatles, concerts with the National Youth Jazz Orchestra and performances with the London Symphony Orchestra, in which he would feature his bravura piano playing on Jimmy Webb’s MacArthur Park.

Greco was renowned for his hot temper. He once pushed a piano off stage towards an audience member who refused to extinguish his cigar, and he squared up to the younger singer Bobby Darin, whom he accused of stealing aspects of his act.

Greco last appeared in Las Vegas in November, when he was inducted into the Las Vegas Entertainment Hall of Fame.

He is survived by his fifth wife, the singer Lezlie Anders, seven children and many grandchildren from his earlier marriages to Sally Baionno, Dani Crayne, Margret Kinley and Jackie Sabatino. All ended in divorce.

• Buddy Greco (Armando Joseph Greco), jazz pianist and singer, born 14 August 1926; died 10 January 2017