Webb, now 68, created the role over 30 years ago and will revisit it for eight performances only from 7 to 12 January 2014.
Tell Me on a Sunday is a one-woman show that charts the romantic adventures of an English girl newly arrived in New York.
It was originally performed as an album and then a TV special and later on stage as one half of Song & Dance.
The album Tell Me on a Sunday reached Number One in the charts and the single "Take That Look Off Your Face" reached Number Two.
The St James revival is produced by Robert Mackintosh, with musical supervision by Simon Lee.