He has been dating cookery student Katie, 26, since last year. The two moved in together earlier this year.
Joel's daughter, Alexa, will be Matron of Honour. His model ex-wife Christie Brinkley (from his Uptown Girl video), will reportedly not be attending.
According to ananova.com, the crooner proposed this January, during a romantic getaway, with a five-carat diamond ring.
Joel has been married twice before -- in 1973 to his business manager Elizabeth Weber; they divorced in 1982.
In 1985, he married Christie, but they split in 1994.
The news follows a rough patch in Joel's life.
Two years ago, he checked into rehab, having lost more than 15kg after consuming nothing but red wine for almost two months.
A friend also revealed that a source for the singer's depression was ex-girlfriend newscaster Trish Bergin's wedding. Not too long before rehab, Joel survived a near-fatal accident when he crashed his Mercedes.
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