The Baggies have been in the market for a right-back since allowing Allan Nyom to leave for Leganes, and the West Midlands side have been linked with a number of players who could be available on loan.
However, head coach Darren Moore has opted to sign former West Ham United and Derby County player Mears, with the 35-year-old available on a free transfer having spent the last three seasons playing in the MLS.
Moore told the club's official website: "We're former teammates at Derby and when I heard about his availability and looked at the situation we have in terms of the squad's balance at the moment, it was a no-brainer for me.
"Tyrone has got a wealth of experience and is a very fit footballer. He totally understands the division we are in and I have no doubt about the job he will be able to do for us.
"The mere fact that he has been in the MLS for the past three years is testament to his condition because you have to be physically right to compete in that league."
Mears has not played in the Championship since representing Bolton Wanderers in August 2013.