Poyet was suspended in May and discovered he had been sacked while working as a pundit on live television.
"Despite the extremely disappointing end to Mr Poyet's career with Brighton and Hove Albion, the club would like to acknowledge Mr Poyet's service to the club," the Championship club said on its website.
The League Managers Association said they were surprised by the decision and would continue to support Poyet, who was suspended for an unspecified breach of club discipline.
"We have supported Gus throughout the disciplinary process and will continue to do so as required," LMA chief executive Richard Bevan said.
"We do not consider that the charges against him amounted to gross misconduct. Gus will now reflect on the outcome and discuss options with the legal team. It would, therefore, not be appropriate to make any further comment at this time."
(Reporting by Toby Davis; editing by Robert Woodward)
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