The 30-year-old striker has moved to Selhurst Park on an emergency loan after passing a medical.
Dobbie has played under Palace boss Ian Holloway twice previously, having enjoyed two loan spells with Blackpool in 2010 and 2012.
The Scot played a key role in helping Blackpool twice reach the Championship play-off final, and he also won promotion with Swansea in 2011.
"I know Ian really well and I'd heard there was a little bit of interest and when that became concrete there was no doubt in my mind to come and play for him," said Dobbie, who has made 16 appearances for Brighton this season.
"I've played for him twice at Blackpool and he gets players playing for him, and he's a great man and a motivator, and I just enjoyed working with him every day."
Dobbie joined Palace hours after former Blackpool team-mate Kevin Phillips was also brought in on loan for the remainder of the season.