Javier Hernandez has described his situation at Real Madrid as "frustrating" after playing 590 minutes for the club.
Baldock joins Albion on a four-year deal for an undisclosed fee and is the Championship side's 12th summer signing.
The 25-year-old was League One's top scorer last season, and Brighton boss Sami Hyypia said: "Sam was one of our key summer attacking targets.
"I'm delighted we have now completed the transfer and to be able to welcome him to the club.
"Alongside our existing forwards, he will give us another attacking option and we hope he will continue to score goals for Brighton.
"He's a predator, instinctive in front of goal and his career goal record is excellent. He's played and scored goals at this level, and we are confident he can be a major threat for us."
Brighton have won four of their six games this season, and Hyppia is confident he now has a squad to compete this season.
"I'm really pleased with the work we've done," he said. "We have quality and options across every position, and will allow us to rotate to cope with the demands of the Championship.
"The recruitment work has been excellent and I would like to thank head of football David Burke and his team for the vital role they've played in identifying, scouting and recruiting our targets."