He is currently recovering from a hip injury which kept him out of the World Cup, and is expected to return to action early in the new year.
He said: "I am delighted to sign up for a further three years with my home club.
"In committing for such a period I can focus on the job at hand, getting back to full fitness, while knowing I have the opportunity to make a difference and help towards shaping the future of this squad."
Stander signed a new deal earlier this week, and with O'Donnell following suit, Munster have secured the future of two key members of their back row.
Head coach Anthony Foley added: "To see guys like CJ and now Tommy committing to Munster is great for everyone involved.
"We all know what Tommy is capable of here, and as a dynamic and powerful player we look forward to seeing him back on the pitch soon.
"He leads this group through his work ethic and professional approach so to have someone with those values continue with us bodes well for the future."
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