The Baggies picked up Rosenberg on a free transfer and Clarke was keen to play up his new striker's European credentials.
"Markus is an experienced striker who has scored goals in three of Europe's top leagues, as well as in the top European competitions," PA Sport quotes Clarke as saying.
"Now he is determined to prove himself in the Barclays Premier League.
"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."
Rosenberg scored 40 goals in his time at Werder Bremen.