Wednesday have confirmed the 20-year-old USA-born man has left Hillsborough and has made the move to the newly-created MLS side, who begin their life in the US with their first game against Seattle Sounders on Sunday.
Murphy was awaiting international clearance before completing the move and that has now been granted so the youngster heads back to his home country to join LA FC.
Murphy, who has been a regular in the Development side since signing professional terms with the Owls in July 2016, made just one senior appearance for the club, in the League Cup clash at Cambridge last season.
Burton midfielder Martin Samuelsen will use the international break to recover from illness after pulling out of Norway U21's games.
Jonas Lossl is staying 'optimistic' over Huddersfield's chances of survival this season and has urged his team-mates to 'go for it'.