Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
Blackpool have signed Rochdale full-back Tom Kennedy on loan, while Tangerines striker Francois Zoko has joined Bradford.
Club president Augusto Cesar Lendoiro confirmed Oltra's departure at a press conference held at the club's stadium and promised a swift announcement of his successor at Riazor.
Within hours the club's official Twitter account revealed that former Braga and Sporting Lisbon coach Domingos will take charge of the team until the end of the season.
Oltra and assistant Chema Sanz leave a club at the foot of the Primera Division with just two wins from 17 matches this season.
According to Deportivo's official website, Lendoiro said: "We felt that now was the right time for a change.
"This is a decision which was not taken today, but on Friday, December 21 after the defeat to Espanyol.
"The situation was irreversible. A shake-up was needed, a change of direction that can only come from changing the coach because there are no other possibilities to change the team itself."
Oltra led Deportivo to promotion from the Segunda Division last season, with the team promoted as impressive champions, and they began this season promisingly with an opening win followed by three draws.
However, a severe decline in their fortunes followed and Deportivo went into the winter break on the back of a 2-0 defeat against fellow strugglers Espanyol, leaving them fighting for their lives in the top flight.
They have mustered 12 points so far, leaving them bottom but only three points adrift of the last team in a safe position, 17th-placed Celta Vigo.
Depor also announced that Oltra will attend training tomorrow morning to say a final farewell to the players before then addressing the media.