The Lakers pulled the trigger on the deal Tuesday night when the NBA lifted the free-agency signing moratorium
In return for the aging Nash, the Suns received first-round picks in 2013 and 2015, and second-round selections in 2013 and 2014.
The 38-year-old Nash, an eight-time all-star and two-time league MVP, reportedly will get a three-year contract in excess of $25 million. The Suns will also get $3.1 million, The Arizona Republic reported.
In 16 seasons, Nash has averaged 14.5 points and 8.6 assists in 1,152 games with Phoenix and Dallas. He averaged 12.5 points and 10.7 assists in 62 games last season.
Nash has never won an NBA championship. But in Los Angeles he will be paired with Kobe Bryant, who has won five with the Lakers.