Quiet amid the early chaos in free agency, the Celtics joined the fray by nabbing the 28-year-old forward who averaged 9.3 points and 6.1 rebounds over 26.4 minutes per game last season. He shot 57.4 percent from the field and made 41.3 percent of his 3-point attempts.
The 6-foot-9 Johnson becomes the Celtics' highest-paid player, bumping aside veteran Gerald Wallace and his $10.1 million salary.
Johnson became a free agent after completing his sixth season with the Toronto Raptors. His best season in Toronto came in 2012-13, when he averaged 10 points, 7.5 rebounds and 1.4 blocks.
After losing in the first round for the second straight season, the Raptors had some decisions to make about their roster with Johnson as one of six free agents. Johnson had hoped general manager Masai Ujiri would keep the team's core intact.
"I've been with this team for six years now," Johnson said at the end of the Raptors' season, according to the Toronto Star. "I've seen the ups and downs of the team, and I really like where we are now, compared with the past. It just takes time. I feel like we have the chance to do something special.
"Keep a team together and they grow together, they get better. So I hope everyone comes back."
ESPN.com's Ohm Youngmisuk contributed to this report.