He helped them win their first Premier League and FA Cup Double last season, and enjoyed a close working relationship with manager Carlo Ancelotti.
Chelsea chief executive Ron Gourlay paid tribute to Wilkins when they confirmed the matter had been resolved on their website on Wednesday.
"I am pleased to announce that we have come to a swift and amicable agreement with Ray Wilkins and all unresolved matters have now been settled," said Gourlay.
"I would like to take this opportunity to thank Ray for his service to the club and wish him all the best for the future."
LMA chief Richard Bevan said Wilkins' focus would now turn to getting back into football in some capacity.
"All parties are delighted that an agreement has been reached in a cordial and professional manner," said Bevan. "I am sure that a manager of Ray's experience will be back involved in a managerial or coaching capacity soon."
Chelsea lost their first two games after Wilkins' exit, with back-to-back defeats in the Premier League at the hands of
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