The striker has joined the Baggies on a free transfer but will not play in Saturday's Barclays Premier League trip to Southampton.
He was available after leaving Celtic in the summer following six years in Glasgow.
Malaga and Southampton were interested in the 29-year-old, who joined Celtic from Manchester City in 2008, but the Baggies were Samaras' first choice.
"We've signed a player with vast experience and I'm delighted to welcome Sami to the club," head coach Alan Irvine told the club's official website.
"He has played a lot of football at the highest levels - Champions League, European Championships and World Cups - and the feedback we've got on him, from people like Neil Lennon, states he thrives on the big occasion.
"He will certainly play in plenty of those in the Barclays Premier League.
"Georgios has played in big games for a Celtic team that have often had a lot of the ball and have had to work hard to break the opposition down.
"But he has also shown another side to his game in other matches when they haven't seen as much of the ball."
Samaras joins £10m club record signing Brown Ideye at The Hawthorns this summer and, with Saido Berahino and Victor Anichebe available, Irvine is pleased with his attacking options.
"We have now got four strikers with different qualities who can be used in different ways," added the Scot.
"That's great for us, because we need to have flexibility, the option to approach games in different ways and cover for injuries.
"I'm absolutely delighted with the four strikers we have."
Samaras made 249 appearances for Celtic, scoring 73 goals, and won four Scottish Premier League titles with the club.
He helped Greece to the last-16 at the World Cup this summer and has 78 caps, and nine goals, for the national side.
Samaras cost City £6m in 2006 but scored just 12 goals in 65 games before moving to Scotland.