"It is important for Depor to stay in the Primera division and for this we need the commitment of everyone," Domingos told a news conference after agreeing to take charge of La Liga's bottom club until the end of the season.
"It is a tough job but I like those, and it is for that reason I am here."
The former Portugal international, who turns 44 on Wednesday, led Braga to second in the Portuguese league in 2010, and his side beat Liverpool on their way to the final of the Europa League the following season, where they lost to Porto.
He moved to Sporting last year, but despite leading them to the Portuguese Cup final, he was sacked in February as they struggled to keep pace in the title race.
"We tried to sign him when he was a player with Porto but Tenerife beat us to his signature," Deportivo president Cesar Augusto Lendoiro said.
"We are convinced we will be able to save ourselves."
Promoted Depor were knocked out of the King's Cup at the first hurdle last month, and after managing only two wins in 17 league matches on their return to the top flight, they sacked Oltra on Sunday.
The Galician club is struggling with crippling debts and Lendoiro has said they will be forced into administration unless a deal with the Spanish tax authorities can be hammered out before the end of the year.
Domingos will make his debut at home to fourth-placed Malaga in La Liga on Saturday, when the Spanish league returns after a two-week winter break.