The clothing and food group said Vindi Banga, its senior independent director, would lead a process to identify and appoint the next chairman.
Swannell, 66, will continue in his role until this process is complete.
Under Swannell's watch the board promoted company veteran Steve Rowe to the CEO role. His priority has been trying to turn around M&S's underperforming clothing and homewares business.
"A year ago we chose Steve Rowe as our chief executive. Steve completed a thorough analysis of the business and developed a detailed plan to build a simpler and more relevant M&S," said Swannell.
"This plan is now underway and I feel that it is the right time for the business to look for a new chairman."
In November, Rowe moved to the second phase of his strategy, outlining plans to shut more than 80 stores at home and abroad at a cost of up to 550 million pounds.
Shares in M&S, which have fallen 23 percent over the last year, were up 0.3 percent at 344.4 pence at 1108 GMT, valuing the business at 5.5 billion pounds.
(Reporting by James Davey; editing by Sarah Young)
