The Lakers announced the deal Monday night.
Johnson set career highs when he averaged 9.1 points and 4.4 rebounds while playing in a team-high 79 games last season, including 62 starts. The 6-foot-7 Johnson also shot a career-best 42.5 percent from the field in his first season with Los Angeles.
Johnson, 27, was the fourth overall pick in the 2010 draft by Minnesota. He signed a one-year deal with the Lakers last summer after one season with the Phoenix Suns.