The 35-year-old midfielder will be eligible to play for the Galaxy when the MLS summer transfer window opens on Wednesday.
Having officially announced in January that he was set to end his 17-year career with his boyhood club to join the Galaxy this summer, the 35-year-old midfielder had taken a brief break following the 2014-15 Premier League campaign before arriving in LA.
Last weekend's home game against Toronto FC saw him introduced to the StubHub Center crowd for the first time, as he watched former Liverpool teammate Robbie Keane bag a hat-trick to seal a 4-0 win in front of a sell-out crowd of 27,000.
Speaking to TWC SportsNet at half-time,he said: "The people of LA have made myself and my family feel so welcome. I'm really excited and just wish I could play tonight!
"My first game can't come quick enough. I'm really looking forward to a successful future.
"Already I'm feeling settled and looking forward to playing with the guys. We've already got a good team here and, if I can add something extra to that, I think the future's going to be good."
Gerrard will be eligible to play for the Galaxy when the MLS transfer window opens on Wednesday and is scheduled to make his league debut on July 17, when the San Jose Earthquakes visit for the California Clasico.
His first appearance for the MLS Cup holders could come as soon as this weekend, though, in their International Champions Cup match against Mexican giants Club America.