The Greece World Cup hero had been a free agent since his Hoops contract ran out in July after six years with the club.
But Baggies head coach Alan Irvine beat off stiff competition from clubs across Europe to land the 6ft 4in forward.
Samaras, 29, will wear the No.30 shirt at The Hawthorns as he battles it out with Brown Ideye, Saido Berahino and Victor Anichebe for a starting place up front for the Premier League outfit.
Irvine said: “I’m delighted to welcome Sami. We have signed a player with vast experience.
“He has played a lot at the highest levels and the feedback we’ve got from people like Neil Lennon states he thrives on the big occasion. He will get plenty of those with us in the Premier League.”