The 26-year-old second row moves to the Ricoh Arena having made 163 appearances for Quins following his debut in 2009.
Wasps director of rugby Dai Young told the club’s official website: “Despite still being relatively young, Charlie has plenty of Premiership and European experience under his belt.
“He is a proven operator who has performed well against us on a number of occasions.
“With Joe Launchbury, James Gaskell, Kearnan Myall and Will Rowlands already in the squad we are well-blessed with second rows and adding Charlie to that group further increases competition for places.
“We believe Charlie has untapped potential which we hope our coaches will help him to achieve. We look forward to his arrival and to working with him over the coming months.”
The 6ft 7in lock has won England Saxons honours after also representing his country at age-group level. His arrival bolsters the Wasps ranks after they saw England internationals, back rower James Haskell and fly-half Danny Cipriani, depart for Northampton and Gloucester respectively on Monday.
“After 11 years and over 150 appearances at Quins, I am looking forward to having a new challenge at Wasps,” said Matthews.
“It’s an exciting time to be heading to the Ricoh Arena as they contend for titles and trophies in the upcoming seasons.
“I would like to thank everyone at Quins for their support; I will always have fantastic memories and be very proud of my time at the club.”
The experienced 33-year-old joins Saints on a one-year deal from Aviva Premiership rivals Wasps. Haskell was a member of the Lions squad which toured New Zealand in 2017 and has also represented England 77 times, including at two Rugby World Cups.
“I’m really excited and humbled to be joining a giant of English rugby in Northampton Saints,” Haskell told Saints’ website.
“Having had the opportunity to play against them for many years now, I know this is a club with a proud history and a set of passionate and loyal supporters who always make their presence felt.
“It’s no secret that I want to continue my international career for as long as possible; the only way I can do that is by putting my best foot forward in club rugby and helping Saints fight their way back into contention for silverware.
“There’s a real buzz around Franklin’s Gardens at the moment with the arrival of (director of rugby) Chris Boyd, a new coaching team being put in place and a number of top-quality players also joining the squad. I can’t wait to get started in black, green and gold.”
Haskell made more than 200 appearances for Wasps during two spells, winning both the Premiership and Heineken Cup.
The 6’ 4” player, who has also spent time with Stade Francais, Japanese club Ricoh Black Rams, and New Zealand side Highlanders, can play in any of the three positions across the back-row.
He becomes Saints’ seventh signing ahead of the 2018/19 season.
Northampton’s director of rugby Boyd said: “We’re thrilled to have captured James’ signature for next season as he’s a player that can bring so much to Saints.
“Not only is he a superb leader with bags of experience at the very highest level, but James is clearly still extremely hungry to win trophies in club and international rugby.
“His record speaks for itself and I have no doubt that he will be an excellent fit for Northampton, both in the side and within the club.”
The 30-year-old’s contract with Wasps expires at the end of the season and he has decided to remain in England as he seeks to resurrect his international career.
The Cherry and Whites, who have also signed winger Matt Banahan from Bath ahead of next season, finished seventh in the Aviva Premiership this season and were beaten finalists in the European Challenge Cup.
Cipriani had received offers from France and Japan but to remain eligible for England he needed to stay in the country.
His arrival at Kingsholm will give options to head coach Johan Ackermann with Billy Burns and Owen Williams vying for the number 10 jersey, although Williams can be utilised at inside centre.
Cipriani will also get the chance on the big stage in Europe with Gloucester’s Challenge Cup final appearance earning them a place in the Champions Cup next season by virtue of opponents Cardiff Blues already qualifying through the PRO14.
Cipriani’s replacement at Wasps has already been announced with the capture of New Zealand fly-half Lima Sopoaga.
He will sign off his Wasps career with a play-off campaign as Dai Young’s side face Saracens in the semi-final on Saturday, hoping to advance to a final against Exeter or Newcastle.