The former Liverpool defender got the job in July, following the resignation of Oscar Garcia after Albion lost in the play-off semi-finals to Derby in May.
The Seagulls have won just once in their last 18 Championship matches and are third from bottom, four points adrift of safety.
In a statement on the Brighton website chairman Tony Bloom said: ““Sami offered his resignation, and we reluctantly accepted earlier today.
“Sami has worked extremely hard since joining the club last summer. Despite some good performances, including most recently at Wolves, results haven’t gone as well as we all had hoped and expected.
“Sami is an incredibly honourable man. He remains a hugely respected and very popular figure at our club. He has decided to step down for the benefit of the team and the club.
“We are all very disappointed, but we respect Sami’s decision and we all wish him well for the future.”
In the interim, Nathan Jones, assistant manager, will take charge of the team for the Boxing Day fixture against Reading.