The 29-year-old has signed a contract that will keep him at the Hawthorns until the summer of 2015.
Rosenberg joins West Brom on a free transfer as his contract with Werder Bremen have expired.
West Brom boss Steve Clarke told West Brom’s official website: “I’m delighted to welcome Markus to the club.
“He is an experienced striker who has scored goals in three of Europe’s top leagues, as well as in the top European competitions, and is determined to prove himself in the Premier League.
“Markus will really increase competition for places in the forward areas and hopefully spur on the strikers we already have here.
“He had several other offers this summer but he made it clear that joining West Bromwich Albion was his first choice and we’re really pleased we’ve been able to conclude a deal.”
Sporting and technical director Dan Ashworth added: “We’ve been keeping tabs on Markus for two or three years now and getting a player of his calibre is a real coup for this club.
“He had offers from Spain, Germany, Turkey, Russia and China and we’re delighted he has chosen this club as the next step in his career.
“Markus is quick, has a great work ethic and can play in a couple of different positions.
“He’s scored goals wherever he’s played and gives us a different option to what we’ve already got.”
