The Lakers are expected to send four draft picks to the Suns, first-round picks in 2013 and 2015, and second-round picks in 2014 and 2015.
The deal to sign free agent Nash cannot be made official until the NBA allows signings on July 11.
The 38-year-old will reportedly sign a three-year deal worth nearly $27 million to join forces with Kobe Bryant and pursue a long elusive championship.
He said he had made the decision after discussions with Suns owner Robert Sarver and president of basketball operations Lon Babby.
"After talking with Robert and Lon we've agreed that it's time for both of us to move in new directions," Nash told ESPN. "I approached them and asked if they would be willing to do a sign-and-trade deal with L.A.
"I couldn't be more grateful to the organization and Robert in particular."
Having captured back-to-back league MVP Awards and leading his team to three conference finals during his last eight years in Phoenix, Nash departs a rebuilding Suns team that have missed the last two postseasons.
The Lakers are also trying to recapture their championship form after getting knocked out of the second round of the play-offs two years in a row.
Nash averaged 12.5 points and 10.7 assists while shooting 53 percent for the Suns last season.
He is expected to replace point guard Ramon Sessions, who opted out of his Lakers contract to become a free agent.