Nash, 38, comes to the Lakers from Phoenix in exchange for a first and second round pick in 2013, a second round pick in 2014, and a first round choice in 2015. The Suns also receive $3 million US cash.
The Lakers will officially introduce the two-time NBA most valuable player and eight-time all-star on Wednesday afternoon. The point guard has agreed to a three-year deal reportedly worth at least $25 million.
The Victoria native just completed the eighth season of his second tenure with the Suns, averaging 12.5 points and 10.7 assists while playing just under 32 minutes per game.
The Lakers are looking to return to pre-eminence after consecutive second round exits, the team's worst playoff showings since losing to Nash's Suns in 2006 and 2007. In between, Los Angeles went to the NBA Finals three consecutive times, winning twice.
Nash will form a backcourt with frequent rival Kobe Bryant, the shooting guard selected two spots ahead of him in the first round of the 1996 draft.
Toronto and New York were heavily interested in Nash's services as he headed to free agency this summer. The Raptors made a pitch that included a video narrated by Wayne Gretzky, according to an ESPN.com report.
When the proposed trade was first reported on July 5, Nash expressed happiness that he will be located near his children, who live in Phoenix.