The final at London's Wembley Stadium on May 25 will be just the fourth single-nation championship match in Europe. Real Madrid beat Valencia in 2000, AC Milan defeated Juventus in 2003 and Manchester United edged Chelsea in 2008.
Bayern will be seeking its fifth title, its first since 2001, while Dortmund won its only championship in 1997. Bayern, which already has clinched the Bundesliga title, travels to Dortmund for a league match Saturday night.
While many expected Barcelona to meet Real Madrid in the final, Dortmund defeated Madrid 4-1 in Germany last week and hung on Tuesday for a 4-3 aggregate win.
Missing four-time world player of the year Lionel Messi, hampered by a hamstring injury for the past month, Barcelona showed little offensive spark. Messi started in the first leg but was largely ineffective, and he didn't get off the substitutes bench for the second.
When Xavi Hernandez was taken off in the 55th minute and Andres Iniesta in the 64th, it left Barcelona without its three biggest stars. Barcelona also was missing defenders Carles Puyol and Javier Mascherano and midfielder Sergio Busquets because of injuries, and left back Jordi Alba because of a suspension for yellow-card accumulation.
While Barcelona has an 11-point lead in the Spanish league with five games left, its first season since Tito Vilanova replaced Pep Guardiola as coach will be considered a disappointment because it failed to win the Champions League following titles in 2006, 2009 and 2011.
Guardiola was hired by Bayern in January to replace Jupp Heynckes as coach at the end of the season.
NOTES: Barcelona goalkeeper Victor Valdes became the 17th player to make 100 Champions League appearances.