The Brazilian requested a transfer from Dortmund earlier this week and the Champions League finalists did not want to stand in his way.
"We would like to thank him for five fantastic, successful years and we wish him all the best for his personal future," said Dortmund director of sport Michael Zorc.
Santana, who has appeared 95 times in the Bundesliga and scored six goals, will fill the void left by the retirement of Christoph Metzelder.
"We are very pleased that Felipe Santana has opted for Schalke," said Royal Blues director of sport Horst Heldt.
"He is known for his aggressive tackling, his reliability and his danger in front of goal, while he has known the Bundesliga for five years."
Despite moving between two bitter local rivals, Santana hopes he does not leave behind any ill-feeling at Dortmund.
He said his decision to leave was purely due to his lack of regular football, with Mats Hummels and Neven Subotic the two first-choice central defenders under Jurgen Klopp, while Sokratis Papastathopoulos' arrival from Werder Bremen today has further intensified competition for places.
"It was a tough decision for me to leave," he said on the Dortmund website.
"That is clear by the fact I extended my contract last summer even though I was not playing regularly.
"But I have got to play regularly now if I want my dream of playing in the Brazil national team to become reality, and that is the aim I have."
His last-gasp goal in the quarter-finals of the Champions League against Malaga helped Dortmund eventually reach the final at Wembley.
"It is important for me to thank the fans, my team-mates and the club bosses for the wonderful time I had in Dortmund," he added.