Odegaard struck the winner at Burnley on Saturday.
Via TMW, he told Stadium Astro: "I liked the project, the coach, the club. I want to be part of the team, rebuilding this club and bringing it back to the top.
"It is very important that young players get stability and continuity, I have been looking for it a lot in the last two years."
Odegaard says he's now settled on Arsenal and life in North London. He's ready to put down roots and develop his career with the Gunners.
The Norway captain added: "I have signed a long contract and I hope to stay for many years. It is fantastic to have a stable relationship with your own club."
Odegaard had returned to Real Madrid this past summer after spending the second-half of last season on-loan with Arsenal. With the Gunners, Odegaard made 20 appearances, scoring twice and producing two assists.
Since making the switch to the Gunners, Odegaard has played four games, scoring once and producing one assist. His deal with Arsenal runs to 2025.
- updated September 20
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