United confirmed the Serb's move, the second time he has left the Blues in seven years.
"I am delighted to have joined Manchester United," Matic said in the release. "To work with Jose Mourinho once again was an opportunity I couldn’t turn down.
"I have enjoyed my time at Chelsea and would like to thank the club and the fans for their support. I cannot wait to meet my new team-mates and to start training with them.
"This is a very exciting time for the club and I am looking forward to playing my part in creating more history for this great club."
The switch comes after a fine season for Matic, 28, as Chelsea won the 2016-17 Premier League title.
He was one of the Blues' more startling underperformers as they briefly flirted with relegation before finishing 10th in the Premier League in 2015-16.
But he returned to his best last term alongside N'Golo Kante and under manager Antonio Conte, playing in 35 of Chelsea's 38 Premier League games, netting one goal and providing seven assists, per WhoScored.com.
The arrival in July, though, of Tiemoue Bakayoko at Stamford Bridge hinted at a more limited role for Matic at Chelsea, and he has now opted to depart the west London club.
Red Devils boss Jose Mourinho is clearly confident that the former Benfica man can continue his fine form from last season at Old Trafford.
Matic can be a huge asset when playing at his best, not only as an extra line of defence sitting in front of the back line, but as a starter of attacks from deep after turning over possession.
United will hope he can free up Paul Pogba to unleash his creative side going forward, safe in the knowledge the defence is protected when he does so.
The Serbia international will no doubt be eager to prove that he remains a top-class player who can deliver consistently.