An ex-Arsenal player himself, Ljungberg returned to the club in the summer of 2018 to take charge of the club’s under-23 side but earned a promotion to become part of Unai Emery’s coaching staff a year later.
Following Emery’s dismissal in November last year, the 43-year-old former Sweden international took charge of the club temporarily for six games, winning just once, before Arteta was given the job on a full-time basis.
Ljungberg remained part of Arteta’s coaching set up upon the Spaniard’s appointment and helped mastermind an FA Cup success by beating Chelsea in the final.
"I have decided to leave my first-team assistant coaching role at Arsenal to progress my management experience," Ljungberg told Arsenal's official website.
"I have been involved with this club on and off since 1998 and am grateful for all the opportunities they have given me both as a player and as a coach.
"I wish Mikel and all the team every success for the season ahead. Thanks also to the fans for their constant support and for always being by my side. I hope we will all meet again soon."
Gunners boss Mikel Arteta said: "Freddie has been a really important member of my team since my arrival.
"He did a great job picking the team up when Unai left and we all have 100 per cent respect for him as a man and a coach. I know I'll be facing him on the touchline in the future."
Ljungberg won two Premier League titles and three FA Cups with Arsenal during a nine-year spell as a player.