The midfielder will head to MLS at the end of the current Premier League campaign after announcing last Friday that he would end his 26-year association with the Anfield club.
And Bryant - a two-time NBA Finals MVP - has backed Gerrard to bring further success to the five-time, and reigning, MLS champions.
"Welcome to Los Angeles, welcome to La La Land," he told the Galaxy's official website. "Hopefully that means bringing another championship to the Galaxy, which I'm sure it will.
"I'm looking forward to getting down there and watching you do your thing.
"I've been a fan of yours for a very long time and your versatility, your aggresiveness and your leadership.
"Welcome to Los Angeles. Enjoy and kick some ass in the process. I'll be down there rooting you on my man."
