The deal is for one year and will be for the $5.9 million taxpayer midlevel exception, sources told ESPN's Adrian Wojnarowski.
Schroder, who turns 28 in September, was the last remaining significant unrestricted free agent on the market. He turned down a lucrative extension offer from the Los Angeles Lakers during the regular season, worth north of $80 million, to pursue a bigger deal this summer.
In Boston, Schroder joins a Celtics team with a hole at point guard in the wake of Kemba Walker being traded to the Oklahoma City Thunder, allowing him a chance to boost his value when he will hit the market again as a free agent next summer.
"I'm proud to announce that for the 2021-22 season I'll be playing for the Boston Celtics!" Schroder wrote on Instagram. "This is one of the best franchises in NBA history and it will be a honour to put on the green and white and do what I love! I'm going out there every night and leaving it all on the floor for the city!! Who's ready?"
The Lakers had acquired Schroder in a trade with the Thunder at last year's NBA draft in exchange for Danny Green and last year's first-round pick.
Schroder averaged 15.4 points and 5.8 assists in 61 games -- all starts -- for the Lakers, but he was mired in controversy after he missed 11 days late in the regular season after entering the NBA's health and safety protocols. He told a German publication that he and LeBron James were the only Lakers players to not get vaccinated, before then telling local reporters upon his return that, "I'm the only guy that didn't get vaccinated. I'll just leave it at that."
He then averaged 14.3 points but shot just 40% from the field and 30.3% from the 3-point line in the Lakers' loss to the Phoenix Suns in six games in the first round of the Western Conference playoffs.
"You got to go through the bulls--- to get to the good s---," Schroder told reporters in his end-of-season news conference after the Suns series.
By signing Schroder for the taxpayer midlevel exception, along with signing center Enes Kanter for a one-year minimum deal, Boston now is sitting a little over $4 million over the luxury tax line with 15 guaranteed contracts on its roster.
The Celtics are coming off a disappointing season that saw them finish seventh in the East and lose in five games to the Brooklyn Nets in the first round of the Eastern Conference playoffs. After the season ended, longtime president of basketball operations Danny Ainge stepped aside, longtime coach Brad Stevens took his place and the Celtics hired Nets assistant Ime Udoka to replace him.
Los Angeles, meanwhile, is facing a massive payroll and luxury tax bill of close to $200 million even without Schroder, per ESPN's Bobby Marks, after trading for Russell Westbrook, signing Kendrick Nunn to a two-year contract worth $10 million, re-signing Talen Horton-Tucker to a three-year, $32 million deal and filling out the rest of the roster with one-year minimum deals, including contracts for future Hall of Famers Carmelo Anthony and Dwight Howard.