Peel said: "My move's not about money, as the deal to stay at Llanelli was similar to that offered by Sale - it's about the fact that, not having lived outside Wales, I'd like to experience life in another country for a short period."
The Scarlets have admitted the departure of Peel will leave a huge void in their side.
Chief executive Stuart Gallacher said: "Dwayne has served us admirably through one of the club's most thrilling decades.
"He has been a cornerstone in helping us to develop a formidable European record in that time and in keeping us highly competitive in domestic tournaments.
"We're always pleased to see homegrown talent become international stars - and Dwayne has served Wales and the Lions with great skill and dedication."
Director of rugby Phil Davies, a former coach at Leeds, does not have a problem with Peel's decision and claimed he would welcome the player back in the future.
Davies said: "He has been outstanding for us in the Magners League and Heineken Cup and will be a credit to his new club. Having never been based outside Wales, this will be an exciting adventure for him.
"I believe he would like to return to Wales and we'd be delighted to talk to him in the future about him coming home to the Llanelli Scarlets."