The Lakers announced Young's decision on Wednesday.
Young, 32, faced a deadline of June 21 to make a decision on his option. The 10-year veteran guard, who averaged 13.2 points in 60 games last season, will hit the open market July 1.
In four tumultuous seasons with the Lakers, Young started 71 of the 220 games he appeared in, averaging 24.5 minutes and 13.1 points per game.
The Los Angeles native realized a childhood dream by joining the Lakers, but Young's tenure has coincided with the worst four-year stretch in the history of the 16-time NBA champions.
After struggling on the court during the 2015-16 season and enduring upheaval in his personal life due to an infamous video scandal with then-rookie D'Angelo Russell, Young enjoyed a career revival last season under new coach Luke Walton.
The Associated Press contributed to this report.