Slade, 48, left League One rivals Yeovil Town last month after a disagreement over funds.
Seagulls chairman Dick Knight told the club's official website: "Russell was on my key-candidate shortlist from the beginning, his CV speaks for itself.
"He impressed when I first met him, he has the confidence to make things happen and I know he gives that to players.
"He has an excellent record and I am delighted to welcome him to the club. Dean White and Bob Booker have done an excellent job in the last fortnight and Russell is happy to work with them to ensure continuity in the coming weeks."