In a report, Ljungberg said he had taken the decision to leave “to progress my management experience”.
Ljungberg had a spell in interim charge following the departure of Unai Emery in November 2019 and stayed on the coaching staff after the appointment of Mikel Arteta.
Ljungberg also coached Arsenal’s under-15 and under-23 squads.
As a player, he made 326 appearances for Arsenal and was part of the Premier League-winning Invincibles side of 2003-04.
“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,” said Ljungberg.
“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.”
Arteta added: “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% respect for him as a man and a coach. I know I’ll be facing him on the touchline in the future.”
Arsenal technical director Edu revealed Ljungberg had “various opportunities over the last 12 months and stuck to the job at Arsenal”, adding: “Now he has the opportunity to consider other options, and it makes sense for his career at this time.”