The 29-year old Scottish striker has signed a three-year deal, joining from Swansea City for an undisclosed fee.
Seagulls boss Gus Poyet was looking forward to having Dobbie at his disposal as he feels he is a very capable goalscorer.
"He is a quality striker, who will complement our existing forwards and give us different attacking options," Poyet told the club's official website.
"He has great quality which will unlock defences and I have no doubt he will also score plenty of goals.
"He has played and proven himself at this level and in the Premier League. His goals helped Blackpool win promotion in 2010 and he returned on loan to help them reach the play-off final last season."