The Welsh club acquired by actors Ryan Reynolds and Rob McElhenney in November 2020 got the movie-script ending they craved last month as they returned to the English Football League as fifth-tier champions with a 3-1 win over Boreham Wood on April 22.
"We've enjoyed meeting supporters who have travelled over from America to visit us this season, and it will be a fantastic occasion to play against American opposition in front of more of these new fans," manager Phil Parkinson said in a statement.
The clash with LA Galaxy II will take place on July 22. Two other U.S. fixtures have already been confirmed, with Wrexham set to take on Chelsea in Chapel Hill, North Carolina, on July 19 and Manchester United in San Diego on July 25.
The squad will also be rewarded with a trip to Las Vegas, sources told ESPN on Tuesday.
Wrexham have attracted plenty of attention in the U.S. thanks to their A-list owners' star power and their popular Disney+ docuseries "Welcome to Wrexham."
The National League champions are due to show off their title-winning trophy to the team's supporters in a homecoming parade through the streets of Wrexham on Tuesday after ending the season with a record 111 points following Saturday's 1-1 draw at relegated Torquay United.
Parkinson's team will discover their opening day opponents in League Two when the fixtures for next season are announced June 15.