News of Garcia's departure from the Championship club broke on Monday, a day after they bowed out of the play-offs.
Brighton lost 4-1 at Derby County on Sunday, leading to a 6-2 aggregate defeat as they exited the post-season at the semi-final stage for the second year in a row.
And just like this season, they will have to start with a new manager after Garcia's decision to walk out.
The Spaniard – who won 21 of his 51 games in charge this season – said he had made his mind up some time ago, and that it was not with another job in mind.
In a statement released on Brighton's official website, Garcia said: "The club has been aware of my thoughts for several weeks and during this time I have had discussions with both the chairman, Tony Bloom, and chief executive, Paul Barber.
"I have enjoyed my time with the club but, although I do not have any immediate plans, I have decided to move on.
"I'm very proud of this season with Brighton. The Championship is a very difficult and competitive league but our record this season has been very good.
"I wish Brighton every success for the future."
Barber thanked Garcia for his efforts and added that the search for his replacement would begin quickly.
"On behalf of the club, I would like to thank Oscar for his efforts and to wish him all the very best for the future," he said.
"The chairman and the board will now begin the search for Oscar’s successor."
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