The 34-year-old last week announced his intention to leave Anfield at the end of the season, after a 26-year association with the Merseyside team.
Gerrard subsequently confirmed he would move to America and Galaxy emerged as strong favourites for his signature.
And the deal now looks a formality with Galaxy coach Arena stating that Gerrard will move to LA in July.
"Steven Gerrard arrives in July and by then we will certainly have a plan available," Arena is quoted as saying by The LA Times.
"He's a player of quality. I'm not concerned about how he's going to fit in with our team.
"We have a club now with a proven history of success. All those things go hand in hand in making LA Galaxy a very attractive team for players such as Steven Gerrard."
Gerrard has been a talismanic captain at Anfield, skippering Liverpool to UEFA Champions League success in 2005 and the FA Cup in 2006.
The Premier League title has proved elusive for the former England captain, though, and he stated his decision to leave was based on the fact he would have limited game time next season.
Gerrard believes a move to LA will now offer him the chance to add more medals to his career.
"I want to finish my career very strong," he said. "I want to add some more medals and trophies to my collection.
"I think it's a match made in heaven really. One of the reasons I chose the LA Galaxy was because of the success they've had recently. But also the plans for more success in the future."
MLS Cup winners Galaxy have been searching for a marquee replacement for former United States international Landon Donovan, who retired at the end of last season.
The signing of Gerrard will see him reunited with former Liverpool team-mate Robbie Keane, who was voted MVP in the MLS last season.
