The Norwegian 22-year-old offensive midfielder played with Alexander Isak in Real Sociedad last season and did so well that he was called back to Real Madrid.
But in the big club it has not come loose and Ödegaard has had a hard time with minutes of play.
For a while it was rumored that he would be loaned back to Isak's club.
But on Wednesday, he was presented by Arsenal.
Ödegaard is applying for a loan that extends until the summer.
- I like the club and have always liked how they play. I like everything about the club and how the coach wants to play, it is a club that suits me well, I think, says the Norwegian to Arsenal's website.