The 25-year-old former Manchester United youngster departs after making just two appearances in his two years on Wearside.
He spent last season out on loan in League One with Wycombe Wanderers and Cambridge, and he will now return to the third tier after joining newly-promoted Wimbledon on a three-year deal.
Speakman said: “Nathan has been an outstanding professional throughout his time at Sunderland AFC, playing an important role within the squad and the dressing room.
"Although injuries disrupted his playing time whilst on loan last season, he ended the campaign strongly.
"This is a step he’s ready to take and his professionalism and work ethic will ensure he has an excellent platform to build from at AFC Wimbledon. We all wish him well.”
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In a statement, the [Black Cats](http://www.thenorthernecho.co.uk/sport/football/sunderland) said: "All at Sunderland AFC thank Nathan for his contribution and wish him the best of luck in the next chapter of his career."
After being on the fringes at the Stadium of Light and enduring an injury-disrupted campaign last term, Bishop is looking to establish himself at Plough Lane.
He said: "The manager, Bayzo (Ashley Bayes, goalkeeper coach) the staff and players were a massive part of me joining this fantastic club.
"Then I heard about the fans - I am delighted to be here and cannot wait to give everything to the people who built this place brick by brick. Up the Wombles!".
Boss Johnnie Jackson said: "We are really pleased to get a goalkeeper of such quality with real experience, he's played for some big clubs so we know exactly what we are getting and as always Bayzo will get the best out of him.
"We are really happy with Nathan and Joe and the goalkeeping department we now have here."
Craig Cope, Wimbledon's director of football, said: "We are delighted to have Nathan join. He's a goalkeeper with real pedigree who can come and work with Bayzo and Joe and really progress alongside the football club."