The Argentine ended his seven-year stay at Newcastle this summer, but has quickly found a new club in La Liga, subject to passing a medical.
The former Argentina international was a big fan favourite at Newcastle after staying with the club to help them back into the Premier League in 2010, not to mention battling back from testicular cancer to assist the first and score the second goal in a key win over West Ham on the final day of last season that helped secure their stay in the top flight.
Gutierrez moved to St James's Park in 2008 from Mallorca, meaning he is returning to play in Spain in what is likely to be the twilight of his career.
There was some criticism in how Newcastle released both Gutierrez and Ryan Taylor at the conclusion of the Premier League season, with it revealed by the players that they were informed of the decision over the phone.
He has signed a one-year contract at the Riazor, and will now travel to the club from Argentina where he had been visiting recently, says the Deportivo site.