Davies hopes the new contract will enable him to push on with his international career as well as helping the younger players at the Liberty Stadium.
"I'm really pleased to have signed a National Dual Contract and to be linking up with the Ospreys," he said.
"The opportunity to return to Wales on a NDC was too good to turn down, the contracts focus on getting the best out of the players and provides support on and off the field and that is really important.
"I'm excited to be joining the Ospreys, it will be a fresh start for me, the region has big ambitions and I want to play a part in that.
"It will be great to team up with the likes of Alun Wyn and the wealth of young Welsh second rows at the region.
"I'm not returning to Wales to retire, I want to push on and the NDC and the Ospreys allow me to do that."
Davies made his international debut in 2009 and is part of this summer's squad to tour New Zealand.
He spent nine years at Cardiff Blues before making the switch to Wasps, who travel to Exeter in the Premiership play-offs this weekend.
Wales head coach Warren Gatland said: "It is great to see Bradley returning to Wales to play his club rugby and to have signed a NDC.
"It is important we create an environment that is attractive to our players and I believe with the number of players retained and returning we are getting on the right track."
Davies will link up with fellow international Alun Wyn Jones at the Ospreys but faces competition from Lloyd Ashley and Rynier Bernardo as well as youngsters Adam Beard, Matthew Dodd and Rory Thornton for a starting spot.
Andrew Millward, Ospreys Managing Director, added: "It is essential that we are able to start building this kind of strength in depth in the squad if we are going to be successful over the coming seasons.
"To that regard, we are extremely grateful to the WRU for their support in enabling us to make such a significant addition to our squad."
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