Boro made a move for Munitis last week, along with Racing Santander and Deportivo La Coruna.
Real Madrid agreed to Boro's offer of a year-long loan deal, but the Spanish champions left the decision on which club to join down to the player.
Munitis considered his options and decided to move to Deportivo, disappointing both Boro and Santander.
"In the last few weeks I have a had offers from a few foreign clubs," said Munitis after he put pen-to-paper at La Riazor.
"One of them was Middlesbrough, but I wanted to stay in Spain and the chance to play in the Champions League with Deportivo was an easy choice to make."
Boro made moves for Munitis and Boudewijn Zenden of Chelsea, as they looked to expand their left sided options.
However, neither player wanted to continue his career on Teesside.
