Villarreal announced the arrival of Alcacer on Thursday, with the former Barcelona striker signing a five-and-a-half-year deal and reportedly commanding a club-record fee of €23million.
The 26-year-old Spain international enjoyed a stunning first season with Dortmund, scoring 18 goals in 26 Bundesliga appearances.
However, he has made just nine starts in all competitions under Lucien Favre this season and struggled with injuries, while the arrival of Erling Haaland from Salzburg led to increased competition for minutes.
Alcacer - linked with former club Valencia earlier in the window - has consequently returned to Spain with Villarreal, who are eighth in LaLiga and booked a place in the Copa del Rey quarter-finals on Wednesday.
It may not be the last of Dortmund's activity in the transfer window, with Can close to arriving from Juve.
Germany international Can was left out of the Bianconeri's Champions League squad this season and has made just eight appearances in all competitions, two of which have come from the start.
Dortmund sporting director Michael Zorc told a news conference on Thursday: "Well, the transfer window isn't open much longer and I don't like to provide any updates until something is final.
"We are talking with the player, this is no secret. But a decision hasn't been made yet."