The League One strugglers sacked Russell Slade earlier this month following a disappointing start to the season.
Poyet has agreed a deal until the end of next season, and will be unveiled at the club on Tuesday afternoon.
New boss: Gus Poyet has been appointed the new Brighton manager
The club's new assistant manager will be former Ipswich and Tottenham defender Mauricio Taricco.
Chairman Tony Bloom said: 'Gus is one of the best up and coming young coaches in this country and we are delighted to give him his first opportunity in management.
'His credentials are exceptional and all of the reports we have had on his coaching ability are outstanding.
'I am certain he will be a big success with the Albion, and I would like to take this opportunity to welcome both Gus and Mauricio to the club.'
Poyet was number two to Juande Ramos at Spurs and second in command at Swindon and Leeds under Dennis Wise.
He is expected to take charge for Brighton's game at Southampton on Sunday.
Former Reading boss Coppell turns down chance to take Brighton helmBrighton sack manager Slade after just eight months in charge of the Seagulls
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