General manager Mitch Kupchak made the announcement. Terms of the agreement were not released, although multiple reports have it at just under $1 million for one year.
"I'm happy to welcome Wesley back to our team and am excited to see him develop further after taking such great strides last season," Kupchak said.
Johnson, like many other young Lakers last season, had a breakout year playing under former head coach Mike D'Antoni. Johnson averaged career highs with 9.1 points and 4.4 rebounds per game while appearing in a team-high 79 contests.
A four-year vet out of Syracuse, Johnson spent his first two seasons with the Timberwolves after they made him the fourth pick in the 2010 NBA draft, and a year with the Suns before signing with Los Angeles last offseason.