Dortmund, who missed out on the Bundesliga title last season after dramatically slipping up on the final matchday, needed an 88th minute goal by Donyell Malen to beat Cologne 1-0 in their opener.
Last week they managed only a 1-1 draw at VfL Bochum with their attack looking toothless for much of the game.
Fuellkrug, who passed a medical late on Thursday, topped the scorer list last season with 16 goals, the same number as Christopher Nkunku.
"Thanks to strong performances he has become a pillar in attack for the national team," said Dortmund sports director Sebastian Kehl.
"I was extremely happy when the offer came because the step to this club was what I was wishing for," Fuellkrug said.
Persons:
Niclas Fuellkrug, Patrik Stollarz, Donyell Malen, Christopher Nkunku, Sebastian Kehl, Fuellkrug, Karolos, John Stonestreet
Organizations:
Soccer Football, Bundesliga, Werder Bremen, FC Cologne, Rights, Borussia Dortmund, Germany, Dortmund, Cologne, VfL Bochum, League, Thomson
Locations:
Weser, Stadion, Bremen, Germany, Qatar