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Costello will perform his full-length orchestral work Il Sogno - which combines classical and jazz styles - during the first half of the concert.
Following an interval he will return to play a selection of his pop hits.
In 2004, Costello recorded Il Sogno with the London Symphony Orchestra and released the music as a 24-track album.
Italian dance company Aterballetto originally commissioned the orchestral work in 2000 for their production of A Midsummer Night's Dream.
The eight-date tour of the US gets under way in San Francisco on 27 March and ends in Atlanta on 13 May.
Oscar nomination
Costello, 51, scored his biggest UK hits with songs including Oliver's Army and I Can't Stand Up For Falling Down in the late 1970s and early 1980s.
He made his musical name with his post-punk band The Attractions. The group enjoyed a string of chart hits in the late 70s, including Watching The Detectives and Accidents Will Happen.
Costello has also composed music for film and television.
He was nominated for an Oscar for his work on the film Cold Mountain in 2004, while his theme to 1991 TV drama GBH won him a Bafta award.
He has also picked up two Ivor Novello songwriting gongs and a Grammy award during his 25-year career.
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