The influential Norwegian midfielder, who was Arsenal’s player of the season last campaign, has committed his future until 2028.
The 24-year-old initially joined on loan from Real Madrid in 2021 and said he has found his “home” at the Gunners.
“Signing a new contract was a really easy decision for me for lots of reasons,” Odegaard said.
“Mainly what we are doing right now as a club is special, and I want to be a part of that. I’m really excited for what’s to come here. I’ve found a place where I can be really settled and call my home.
"My story is a bit different maybe, as I moved around different clubs since I was 16. At Arsenal, since the first day, I’ve felt great and this is definitely my home now.
“I just want to say thanks to everyone working at the club and of course, our fantastic supporters. I will continue to give everything to bring success to this club in the years to come.”
He scored the fourth goal of Arsenal’s 4-0 win over PSV on Wednesday as the Gunners marked their return to the Champions League with a commanding victory at the Emirates, six years after their last appearance in the competition.
“It just shows what we’re doing as a club. People want to be here as part of the project.
“What we’re doing is really special and the players see what the manager wants to do and how the club is progressing, the connection we now have with the fans.
“I think it’s a no-brainer for the players to be part of that. With so many hungry young players, it’s a great place to be.
“Of course, it’s a good thing. You see the players around you want to be a part of what we’re doing and it shows just how connected we are as a team.
“All the players want the same thing, they want to stay for a long time and really fight for the club and win things together. It shows the family feeling we have.”