The contract could be worth as much as $3 million, sources told ESPN NFL Insider Adam Schefter.
The deal was announced Sunday and will become official when he passes a physical.
"We just got better as a team," Ravens general manager Ozzie Newsome said. "To have a successful season, you have to have quality depth across the board. We just added great depth to the interior of our offensive line with Andre."
Gurode was signed to play behind six-time Pro Bowl center Matt Birk, who had surgery on his left knee at the beginning of training camp.
Gurode was cut by the Cowboys last week.
Information from The Associated Press contributed to this report.