He announced his intentions on his website (www.klitschko.com) and in a statement on his Instagram account.
The 39-year-old Klitschko said: "I have a pre-season Christmas gift for Tyson Fury and all boxing fans around the world: I will be making use of my contractual option for a rematch against Fury. So... the fight of 2016 is in the making."
He said on his website that he felt "really frustrated" immediately after Saturday's fight but added: "After some short nights, I now know that I want to show that I am much better than my performance on Saturday. Failure is not an option."
Fury's trainer and uncle, Peter Fury, told Sky Sports television that his camp were happy with the rematch. "It's in the contract. We're very happy to take it."
Details have still to be worked out but the trainer said London's Wembley Stadium next year was a possibility.
(Reporting by Neville Dalton; editing by Clare Fallon)
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