The former Hoops skipper spent the second half of last season on loan at the club and on Tuesday made the move permanent.
McManus joins forces with former Celtic boss Gordon Strachan, as well as old team-mates Barry Robson, Chris Killen, Willo Flood and Scott McDonald.
A statement on Celtic's official website read: "Celtic Football Club has bid farewell to their former captain, Stephen McManus, after ten successful years at the Hoops.
"The 27-year-old has joined Gordon Strachan at Middlesbrough after spending the remainder of last season on-loan to the Championship side.
"McManus was a product of Celtic's youth academy before making his first-team debut in 2003 and was handed the captaincy on a permanent basis when Neil Lennon left the club four years later.
"The defender meets up with former Celts Scott McDonald and Willo Flood as he signs a three-year deal with the English side.
"Everyone at the club offers Stephen and his family their sincere best wishes for the future and thanks him for his great contribution to the club."
McManus, who had earlier completed a medical on Teesside, is the fourth man to join Boro this summer following Andy Halliday, Kris Boyd and Nicky Bailey.
The Scotland international made 16 appearances for Boro last season in an impressive spell which persuaded Strachan he could do the job on a permanent basis.
McManus becomes the latest Old Firm recruit to head for the Riverside, following in the footsteps of the Celtic quartet and Rangers striker Boyd.
He could soon be joined by Rangers midfielder Kevin Thomson, who headed for the North-East on Tuesday to discuss a proposed switch from Ibrox.
McManus was delighted to have completed his move after whetting his appetite for English football last season.
He told Boro's official website: "I was lucky to have 12 great years with Celtic, right from leaving school. I was sad to go but it was the right time for me to move on.
"I really enjoyed my time at Middlesbrough last season. Everyone has been great with me here right from the off.
"The manager made it clear to me how much he wanted me to come here and in any line of work, you want to go where you are most wanted.
"In terms of the decision, I wanted to know what the manager's thoughts and plans were for the future.
"Obviously the signings the club has already made are impressive, while it's clear from speaking to him that the manager is ambitious.
"All the lads here are ambitious. This club should be in the Premiership, so promotion is the aim.
"The Championship is a tough league, but the aim is to go up. It's a big challenge for all of us, but one I am looking forward to."