The 23-year-old had passed a medical and signed a five-year contract until June 2017, the club said in a statement on their website.
"Alvaro Dominguez was our ideal candidate for the position of left-sided centre-back," sporting director Max Eberl said.
"He was a fixture for Atletico, won the Europa League in 2010 and 2012 and recently made it into the Spanish national team," he added. "We are proud that he has chosen Borussia."
Madrid-born Dominguez came through Atletico's youth academy and made his debut for the La Liga side in a Champions League match against Liverpool in October 2008.
He was in the preliminary Spain squad for Euro 2012 but was not included when coach Vicente del Bosque announced his final 23-man roster.
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