The 23-year-old has signed a three-year contract and joins Sebastian Mielitz in a battle to take the jersey left by Wiese following his transfer to Hoffenheim.
"It is great that we have been able to sell Werder to Raphael Wolf," said Bremen coach Thomas Schaaf.
"We now have very good candidates for the goalkeeper position and it is going to be a high-level competition for that position, which is what we wanted."
The German goalkeeper was a regular for Kapfenberg in the Austrian Bundesliga last season and made a total of 104 appearances for them over the last three years.
He is now ready to take the next step in his career.
"I desperately wanted to get back to Germany and the offer from Werder was the best thing that could have happened to me," he said.
"It is a good club with a lot of tradition and even more achievements, and we want to build on that."
Wolf was previously contracted to Werder's northern Germany rivals Hamburg, although he failed to made a senior appearance in five years spent mainly in their youth and reserve teams.