It marks a return to England for the 35-year-old defender after spending the last three years in Major League Soccer with Seattle Sounders, Atlanta United and Minnesota United.
Mears is set for an immediate debut under the management of ex-Derby colleague Darren Moore as West Brom face Mansfield Town in the Carabao Cup later today.
"We're former team-mates 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," Moore explained to WBA.co.uk.
"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. He's got massive experience and I'm pleased to have him here."