The bronze figure by Scottish sculptor David Annand stands at the entrance to The Stables Theatre in Wavendon, Milton Keynes.
It was commissioned by trustees of the Wavendon Allmusic Plan (WAP), which he set up with his wife Cleo Laine to oversee the theatre's work.
She said it was a "fitting" honour.
Born in 1927, Sir John's career as a performer, composer and conductor spanned more than 50 years and earned him a CBE as well as a knighthood. He died in 2010.
He was 1949 Musician of the Year in Britain and worked as a leader of both small and big bands.
His hit records included Experiments with Mice in 1956 and African Waltz 1960, while his movie scores included those for Saturday Night and Sunday Morning and Modesty Blaise.
Sir John also served as musical director for artists including Nat "King" Cole and Ella Fitzgerald.
Together with Dame Cleo, he turned outbuildings at their home into a venue for concerts and educational music activities and founded a charity to run it in 1969.
The current Stables Theatre opened its doors in 2000.
WAP chairman Stephen Clarke said: "He established the trust 45 years ago with the vision of making all music genres accessible to all people.
"That vision lives on and the current trustees hope that David Annand's wonderful sculpture will serve as a fitting tribute to their legacy, as well as bringing much pleasure to all our visitors."
Dame Cleo said: "It's fitting that John's contribution to music and music education has been honoured by the charity we established 45 years ago."
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