Asier Illarramendi said his time at Real Madrid had not worked out as he had hoped after completing a return to Real Sociedad.
Illarramendi joined Madrid from Sociedad in a €38.8 million deal in 2013 but struggled to win a regular place under then coach Carlo Ancelotti.
And with new Bernabeu manager Rafa Benitez having paid €30m for Croatia international Mateo Kovacic, 25-year-old Illarramendi rejoined his old club in a move reported to be worth an initial €16 million.
Speaking at his presentation at the Anoeta, he said: "Things did not go as well as I would have liked.
"You learn from everything, the good and the bad. It was not so bad, though. In two years I won four trophies [the Copa del Rey, Champions League, European Supercup and Spanish Supercopa, although he played only eight minutes across those finals]."
When it became clear Ilarramendi would be leaving Madrid, he was linked with clubs including Liverpool, Tottenham, Juventus, Inter Milan and Southampton.
"I had different possibilities to weigh up, but I had a pretty clear decision," he explained. "I spoke with my people and took the decision two days ago."
Adding that he had already had a chat with his new boss David Moyes, he said: "I was with the coach for a while -- and I already know I will have to learn more English."