The 23-year-old, who was involved with Harlequins at youth level before heading to University in Wales, joins from Cardiff.
He struggled to establish himself in the Cardiff first team after joining from Bedwas but is looking to kickstart his career in London.
Cooper-Woolley captained Cardiff University to Welsh Varsity triumph at the Millennium Stadium in 2012, before succumbing to injury which saw him miss most of this season, where he was expected to play a strong role with Cardiff.
He has previously spent two seasons in the Welsh Premiership playing with Bedwas and the Dorking native will return to English rugby over the summer to London Wasps under Dai Young’s guidance.
Young said: “We’ve got some very talented young props here with the likes of Phil Swainston and Will Taylor stepping up and doing a fine job this season.
"I saw Jake playing at Cardiff University and was very impressed and he’s a young English boy who wants to improve. He’s got a strong physical presence and has played at both loose and tight head.”