The 35-year-old looks likely to make his debut in Tuesday's Carabao Cup tie against Mansfield.
Mears played with Preston, West Ham, Derby, Burnley and Bolton earlier in his career.
He then headed off to the MLS in 2015, where he played for Seattle, Atlanta and Minnesota.
Mears has now agreed a rolling contract with the Baggies until January.
Darren Moore told the club website: "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."
"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."