The experienced point guard, who became a free agent on July 1, was reportedly being pursued by a Miami Heat team that already has All Stars LeBron James, Dwyane Wade and Chris Bosh.
"At the end of the day, there's one person I could not turn away from. Kobe Bryant asked me to stay but supported whatever decision I made," Fisher said in a statement on Monday.
"While this may not be the most lucrative contract I've been offered this offseason, it is the most valuable."
The 35-year-old Fisher, drafted in the first round by the Lakers in 1996, averaged 7.5 points and 2.5 assists per game last year. He upped his production in the playoffs with 10.3 points and 2.8 assists per game.
(Writing by Frank Pingue in Toronto; Editing by Julian Linden)
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