The Sky Bet Championship club parted company with Monk on Saturday after the 2-1 victory at Sheffield Wednesday left them ninth in the table.
Pulis has been out of work since November when he left Premier League strugglers West Brom, but the Teesside club have now announced he will be the man they hope can lead them to promotion.
The 59-year-old will watch the Boxing Day game against Bolton at the Riverside Stadium from the stands, with academy manager Craig Liddle taking charge of the team.
“We’re delighted to appoint Tony as our new manager. His experience and knowledge speaks for itself and he has a tremendous track record,” said Middlesbrough chairman Steve Gibson in a statement on the club’s official website.
“We’re excited by this appointment and by what Tony can bring to this football club. There was strong interest from two other clubs, and we’re delighted Tony has decided to join us.
“There’s no disguising that 2017 has not been a happy year for any of us, but we’ve refocused and we’re looking forward to the future.”
Pulis, who had been linked with the Swansea job following Paul Clement’s departure, is expected to take charge for the first time against Aston Villa at the Riverside on Saturday.
When the Welshman left West Brom last month he had indicated he would take a little break from the game but has returned to management quickly because he felt the set-up at Boro felt right.
“I wanted a challenge - a real challenge - and this reminds me so much of Stoke when I went there with Peter Coates,” said Pulis. “Steve Gibson is a football man who understands the game. I have great respect for him as a person and an owner.
“I really am looking forward to this. The immediate challenge is finding out about the football club and as a team we have to get as many points as we can, as quickly as we can.
“I wanted to come at this time because we have so many games in a short space of time, and I can assess everything.”
Pulis has taken charge of over 1,000 games since his 25-year managerial career began at Bournemouth in June 1992. Middlesbrough will be his ninth different club but he has not managed outside of the Premier League for almost a decade.
Pulis got Stoke promoted from the Championship in 2008 - his second promotion after getting Gillingham up from the old Third Division in 1996.
He also took Stoke to an FA Cup final in 2011 during his second spell in charge but the Potters were beaten 1-0 by Manchester City at Wembley, although it meant they did qualify for the Europa League the following season.