The 30-year-old Stimpson has enjoyed a hugely successful spell at Leicester, winning the Zurich Premiership for four of those, as well as two Heineken Cups.
"I have had five-and-a-half brilliant years at Leicester and this was an incredibly hard decision for me to make," said Stimpson.
"I've loved every minute of my time at the club but this is an opportunity that I can't turn down.
"It's a chance to learn a different way of playing with a different set of players in a totally different culture. I've always said that I wanted to play abroad at some stage, although I'm not ruling out a move back to England.
"I am continuing to enjoy every game for Tigers, and maybe I'll return one day as a player or even as a coach."
Stimpson helped Leicester to beat Newcastle Falcons in Friday's Zurich Premiership match at Welford Road, and Tigers' Director of Rugby Dean Richards hailed Stimpson's talents after news of the move.
"Obviously we are disappointed that Tim has decided to leave us after playing such a large part in our recent success," said Richards.
"I would like to keep him here but he sees this as an incredible opportunity for him and I won't stand in anybody's way.
"We could have insisted that he see out the rest of his contract until the end of June but Tim had made up his mind to go, and we agreed that the beginning of December would be the best date for all concerned."
The former Newcastle and West Hartlepool player has picked up 19 England caps as well as touring with the 1997 Lions, but has fallen out of favour in the international reckoning of late – his last cap coming back in November 2002 against South Africa.
He was even left out of England's 60-man elite squad when it was named this week, but now has a whole new set of challenges to look forward to, with the Catalan side having reached the Heineken Cup Final last season, losing to Toulouse in Dublin.
But Perpignan have not rested on their laurels, and have embarked on a major recruitment drive over the last few months, with Wallaby centre Daniel Herbert, England wing Dan Luger and Munster lock Mick O'Driscoll being among their new signings.
Added to that, Leicester props Franck Tournaire and Perry Freshwater have also signed with the club, who under coach Olivier Saiset, are set to mount a serious challenge on the domestic title when the league starts properly after the Rugby World Cup.
His departure from Leicester could however leave a hole at the back if they do not recruit swiftly, after the recent injury to Ireland fullback Geordan Murphy, who broke his leg while on Test duty against Scotland earlier this month, and could now face a lengthy spell on the sidelines.