Team spokesman John Black on Wednesday confirmed Bryant's decision. The MVP of the NBA Finals had until Tuesday to become an unrestricted free agent.
Now the Lakers and Bryant's agent will negotiate a contract extension. He has spent his entire 13-year career with the team, winning four NBA championships.
On June 19, Bryant said, "I'm not going anywhere. I know I ain't going nowhere, so it's just a waste of our breaths just talking about it."
Bryant is scheduled to make $23 million next season.
The Los Angeles Times reported late Tuesday that Bryant will sign a three-year extension with the Lakers sometime this month. Bryant could make $47.8 million over the next two years and another $86 million to $91 million with the extension, with the difference depending on the future salary cap, the newspaper reported.
Ariza made $3.1 million last season and his play in the NBA Finals against Orlando is expected to earn him a major pay raise. Odom made $14.1 million last season and is expected to have to take a substantial pay cut to stay.
Information from The Associated Press was used in this report.