The player is set to join the Premier League club on a loan deal until the end of the season.
Apparently, Real Sociedad tried to sign the attacking midfielder as well but the player has decided to join Arsenal instead.
Odegaard needed to leave Real Madrid in order to play regular first-team football and it will be interesting to see if he can make an impact at Arsenal.
Apparently, Mikel Arteta spoke directly with the midfielder and it was a key factor in his decision to join Arsenal.
The youngster is rated highly across Europe and he has been linked with a move to the Premier League in recent years. It remains to be seen whether he can adapt to English football during the second half of the season now.
Arsenal got rid of Mesut Ozil earlier in the month and it seems that Odegaard could be his replacement for the season.
Meanwhile, Arsenal have been offered the chance to sign Christian Eriksen.
Apparently, Inter Milan want a swap deal involving the Danish playmaker and Lucas Torreira.
Torreira is currently on loan at Atletico Madrid and it will be interesting to see if the Gunners are willing to move forward with a swap deal at the end of this season.
Elsewhere, Sokratis has had his contract with Arsenal terminated and the defender is now a free agent.
His former teammate Shkodran Mustafi is now ready to leave the Gunners after falling down the pecking order at the club and he is waiting for offers now.