The 29-year-old, who joined Wasps in 2014 from Cardiff Blues, leaves Wasps after the English Premiership side agreed to release him a year early.
Davies, who has signed a deal through to the 2019 World Cup, hopes his return will further his international career.
"I am excited about returning to Wales and joining Ospreys," he said.
"I would like to thank Wasps for the last couple of years.
"The opportunity to return to Wales on an 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 not returning to Wales to retire, I want to push on and the NDC and the Ospreys allow me to do that."
He is likely to feature for Wasps in the Premiership semi-final against Exeter Chiefs on Saturday, 21 May, before linking up with Wales for their tour of New Zealand in June.
Davies, who made his international debut in 2009, spent nine years at Cardiff Blues and now becomes the ninth player to sign a national dual contract with Ospreys.
Wales coach Warren Gatland commented: "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."
Ospreys managing director Andrew Millward said: "We are extremely grateful to the WRU for their support in enabling us to make such a significant addition to our squad."
Davies has made 37 appearances for Wasps and the English side's director of rugby Dai Young admitted it was a blow to lose the lock.
"We will obviously be sad to see Bradley leave as he is a great character to have around the training ground and has played a key role over the past couple of seasons in helping our pack develop a harder edge," he said.
Wales second row Bradley Davies will return to Wales next season to take up a national dual contract (NDC) with the Welsh Rugby Union and Ospreys.