The club said on Sunday night that they have taken the decision following an investigation by their internal disciplinary panel.
Poyet was told of his sacking by the BBC, for whom he was working as a pundit during their Confederations Cup coverage.
He said: "I think the BBC have a great story forever, because a manager getting the information that he is being released from his employment by the BBC is quite surprising.
"I have had no communication, no texts, no e-mail. I didn't receive anything on my phone, so it is all up to you and the timing.
"The only thing I'm concentrating on is the appeal. I will appeal because it's the right thing to do."
Poyet led Brighton to the play-offs last season but, following their semi-final loss to Crystal Palace, the Uruguayan boss, his assistant manager Mauricio Taricco, and coach Charlie Oatway were all suspended.
Taricco's suspension has subsequently been lifted but Poyet failed to appear at a disciplinary hearing last Monday, although he did attend a re-convened hearing on Thursday.
Brighton have refused to divulge the reasons for the suspensions but, on Sunday night, a day before the players return for the first day of pre-season training, the club released a statement announcing Poyet's dismissal.
It read: "Gus Poyet has been informed today by Brighton & Hove Albion football club's internal disciplinary panel that his employment has been terminated with immediate effect.
"This followed his suspension, an investigation, and a subsequent formal disciplinary process.
Poyet has the right of appeal
"In line with the club's own procedures, and UK employment law, Mr Poyet now has a right of appeal.
"As such, the club will make no further comment on this matter or recent LMA (League Managers' Association) statements at this time.
"Given the close proximity of the new season, the club will, in conjunction with its board, now seek to appoint an interim manager pending the outcome of a possible appeal.
"The interim manager will oversee the initial weeks of pre-season preparation alongside the club's existing staff."
The LMA have backed Poyet in the dispute and say the charges against him are "unfounded" in their opinion.