Odriozola joined Bayern on-loan in January for the remainder of the season.
He told Marca: "I thought it was time to look for a new opportunity. And when the option of a club as legendary as Bayern Munich presented itself, I thought about it calmly and finally made a decision. A footballer has to play and I had no doubts [about joining Bayern].
"I've always said that one season at Real Madrid is worth three at any other club. It's an accelerated masters, not only in a football sense but also in life. Of course, that season was very profitable: I played 22 matches (providing nine assists) and was unlucky enough to get injured in a training session in mid-April that didn't allow me to finish the season."