General Manager Mitch Kupchak welcomed the two-time MVP to the purple and gold family by calling him a thorn in the Lakers' side for most of the last decade.
With Wilt Chamberlain's No. 13 retired, Nash will wear No. 10 on his jersey for his love of soccer, where No. 10 is often worn by playmakers on the pitch.
The 38-year-old is the eighth most accurate three-point shooter of all time and is fifth on the league's all-time assist list.
Nash said he is really proud of being a Laker and looks forward to playing with Kobe and company.
"If I can make the game a little bit easier for him, take a little bit of pressure off him, I think we'll be all the better," said Nash. "If this is his team, we go as far as he takes us and it's our job as a group to make this thing as easy as possible for him. I haven't had a chance to play with many post players in my career so it's going to be exciting and an adjustment, but a good one. Hopefully it'll be seamless."