The 35-year-old will remain a member of the playing staff at the Liberty Stadium, but will regularly sit alongside Clement in the dugout after Claude Makelele, his manager's former No. 2, left to take the reins at Belgian outfit Eupen.
"I am delighted. To have this opportunity is a massive moment for me and my family," Britton said, per the club's official website.
He added: "It's not the end of my playing career. I will still be training every day and will be up for selection. But I will also be in staff meetings and looking to prepare for games from the coaching side."
Britton is a fan favourite at Swansea. He's a veteran of 525 appearances over two spells with the club, and regularly takes it upon himself to educate new arrivals of Swansea's recent history - from its narrow avoidance of relegation into non-league football in 2002-03, to becoming a League Cup winner and top-tier mainstay while under the guidance of fan ownership. He will relinquish his duty as club captain after taking on extra responsibilities, and is currently studying for his UEFA A coaching licence.
In addition to his unique understanding of Swansea, Britton is noted for his exemplary use of the ball. During the 2011-12 term, it was discovered that he had the best passing accuracy in Europe, edging Barcelona's Xavi to top spot with a 93.3 percent success rate.
"Leon has a great relationship with the players and has a superb connection with the supporters of this club," Clement shared. "He knows more than anyone what playing for this club means.
"I have no doubt he will manage the dual role as both a player and coach."