The Championship side's former manager was initially dismissed following an investigation into a breach of contract, with the Uruguayan unsuccessfully appealing the decision
The Uruguayan was suspended in the aftermath of the club's Championship play-off semi-final defeat to Crystal Palace last season for alleged breach of contract, and was subsequently removed from his role as manager in June.
He appealed the original decision, but Brighton have announced that process is now complete with the initial ruling upheld.
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"The panel's decision was delivered to Gus Poyet and his advisers a short time ago.
"The club's internal disciplinary process is now complete. In line with the club's policy to ensure and maintain confidentiality and dignity throughout this process, no further details of the disciplinary or appeal hearings will be released at this time."
Poyet joined Brighton in November 2009 and guided the club to the League One title in 2011, but was unsuccessful in his attempt to take them to the Premier League.