Lawley, a former BBC newsreader and journalist, has presented the show since 1987 and is only the third person to sit in the presenter's chair in its 64-year history.
She informed Mark Damazer, controller Radio 4, of her decision two weeks ago and will stay on until the end of summer presenting her last show on August 27.
"I've had more than 18 very happy years and have talked to some extraordinary people as they revealed themselves through their choice of music. It is one of the best jobs in broadcasting. But it has dominated my professional life and I feel the time has come to concentrate on other aspects of broadcasting and maybe a bit of business too," Lawley said.
During her time on the show, Lawley has interviewed more than 750 "castaways" from the world of sport, politics and culture who choose eight records they would take to a desert island, including Patrick Stewart, Nigel Slater, Stephen Poliakoff, Jarvis Cocker, Menzies Campbell and Kelly Holmes among others.
Damazer said: "I tried hard to persuade Sue to change her mind but to no avail. She started her career as a journalist and is still a journalist at heart. She also has an enormous interest in people. Put these two attributes together and you end up with fascinating and entertaining interviews that are now the hallmark of 'Desert Island Discs'. She will be a tough act to follow."
'Desert Island Discs' began during the Second World War in 1942 by Roy Plomley, who presented the show until his death in 1985. He was succeeded by Michael Parkinson.
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