"The German club will pay Barcelona 2 million euros for the year-long loan and take charge of the player's salary," the Spanish champions said in a statement Tuesday.
Dortmund can buy Alcacer at the end of the loan but Barcelona also have the right to refuse.
Should the forward sign permanently for Dortmund and later be sold to another club, Barcelona would earn five percent of the transfer fee.
Alcacer, who turns 25 on Thursday, joined Barcelona from Valencia in 2016 but failed to earn a regular first-team place with Luis Suarez picked ahead of him for the sole centre forward role.
The Spaniard scored 15 goals in 50 appearances over two seasons, winning La Liga, the Copa del Rey twice and one Spanish Super Cup.
(Reporting by Rik Sharma; Editing by Toby Davis)
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