The 34-year-old, who returned to Scarlets after enjoying a two-year stint with Clermont Auvergne in 2006, has signed a two-year contract with Dai Young's side.
Jones' move continues a trend of Welsh players opting to play their rugby outside Wales, with scrum-half Richie Rees and prop John Yapp revealing they will also leave the principality this summer - swapping Cardiff for Edinburgh.
Rees will take the place of the departing Mike Blair at surprise Heineken Cup semi-finalists Edinburgh, while Yapp, capped 21 times for Wales, will add depth to the Scottish club's front-row.
Jones' departure to Wasps, currently second from bottom in the English Premiership, will allow Wales Grand Slam-winning fly-half Rhys Priestland to take full possession of the No.10 shirt at Scarlets.
The move is likely to push Jones, a late call-up this year's Six Nations squad, further down the international pecking order but the fly-half has no regrets.
"I feel this is the right time to move on at this stage in my rugby career," he said.
"The Scarlets are showing such promise and have plenty to build on for the future with a very talented group of emerging players who are only going to go from strength to strength now.
"I feel very privileged to have been part of this great club for so many years and particularly the new era - with a team that now has so many exciting new players coming through and achieving international honours.
"I hope I've been able to pass on some of my experience for the benefit of our future as a region and helped accelerate the transition of this squad in recent years.
"It's been a huge part of my life being a Scarlet - starting when I was 18 and now leaving when I'm 34 and apart from a couple of years in France its where I've grown up as a rugby player. I've been delighted to be part of Scarlets Rugby throughout and it has been an honour to pull on the shirt every single time."