Turner, 51, spent six years in charge of the Dragons in the Magners League having previously worked with Sale and Harlequins in the Premiership.
He said: "To join a club of Wasps' calibre is a great opportunity for me. Wasps have always been a club I admired and respected and I am delighted to be back coaching in the Premiership.
"The club has clearly put together a strong squad for next season with some highly-talented attacking individuals and I am looking forward to helping shape the structure of how the side plays."
New Wasps director of rugby Dai Young added: "We are really pleased to introduce Paul to our plans for the new season and we believe that he will be an important addition to the coaching set-up.
"He will bring some fresh attacking ideas to the team and I think he can make a big impact in our style of play this season."
Turner left the Dragons in February after publicly criticising the Welsh Rugby Union's handling of the club's players.
He was also involved in a run-in with a journalist as the Dragons' slumped in both the Magners League and the Heineken Cup.
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