Tamas has been looking for a new club since being released from The Hawthorns at the end of his contract this summer.
It returns the 29-year-old to his homeland. In June, he was arrested and jailed after being found drunk outside a block of flats in Bucharest.
In 2011, he and teammate Adrian Mutu were handed life bans by the Romanian FA after reports the pair went out drinking before a friendly match with San Marino.
The ban was lifted just 43 days later.
Tamas joined the Baggies from French club Auxerre in 2010 and made 77 appearances.