The defender appeared in all four of his country's matches at Euro 2012 and following their elimination at the hands of Portugal on Thursday night has now confirmed his move to the Bundesliga.
Gebre Selassie, 25, joins Bremen from Slovan Liberec for an undisclosed fee.
"The decision to join Werder Bremen was the right thing to do," he told the club's official website.
"This is a club with a lot of stability and tradition, who always set their goals high. I would like to emulate here my successful season at Liberec."
Gebre Selassie won the Czech title last season and has signed a four-year deal with Bremen.
"We are pleased that we were able to convince Selassie to join us despite having several other offers," said sporting director Thomas Schaaf.
"He is a very talented right-back who confirmed our good impression of him with some good performances at the European Championship."