The 51-year-old has spent the last six years in charge of Newport-Gwent Dragons having previously worked with Sale and Harlequins in the Premiership.
"To join a club of Wasps' calibre is a great opportunity for me," said the former Wales international. "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 them shape the structure of how the side plays."
Turner left the Dragons in February after publicly criticising the Welsh Rugby Union's handling of the club's players.