The 22-year-old was one European football's hottest properties when he joined Spanish giants Real from Stromsgodset six years ago.
Here, the PA news agency takes a closer look at the Norway international following his switch to the Premier League.
He made his Norway debut aged 15
Odegaard was born in the Norwegian port city of Drammen – around 27 miles south-west of the capital Oslo – in December 1998. Fast-forward 15 years and 253 days and the talented youngster was thrust on to the international stage. He became the youngest Norway player in history – an achievement which still stands – after playing the full 90 minutes of a goalless friendly draw with the United Arab Emirates in August 2014. He has already won 25 caps and claimed his maiden national team goal during a Euro 2020 qualifying draw with Romania in June 2019.
His father joined Real at the same time
Hans Erik Odegaard had a rather less illustrious professional career than his son and never represented his country. However, that did not stop Odegaard senior – who also played as a midfielder, for Stromsgodset and Sandefjord – simultaneously moving to the Spanish capital in January 2015. During transfer talks, the 47-year-old managed to secure a role as a Real Madrid youth coach. He proved to be an adept negotiator and was reportedly earning more than current Real boss Zinedine Zidane, who was then head coach of the club's reserve team.
He is the youngest player in Real's history
Having joined Real a month after his 16th birthday, Odegaard's senior debut for the Spanish side came in May 2015 when he stepped off the bench to replace club great Cristiano Ronaldo. Ronaldo, Real's record goal-scorer, was given a well-earned rest with 32 minutes remaining after hitting a hat-trick in a 7-3 LaLiga demolition of Getafe. The cameo appearance under the management of Carlo Ancelotti meant Odegaard became the youngest debutant in Real's history at 16 years and 157 days old – a record he retains.
He loved Lionel Messi
Odegaard has probably kept quiet about it since moving to Madrid but, according to a former youth coach in his homeland, he was a massive admirer of the star player of his parent club's greatest rivals. Harald Johannessen says the new Gunners man grew up idolising Barcelona and Argentina forward Lionel Messi. "He was always looking at Messi, I remember that," Johannessen said in a 2019 interview with These Football Times magazine. "He loves Messi, so that was a little bit strange – he loves Messi and he goes to Real Madrid."
He is no stranger to a loan move
Odegaard was being chased by top clubs across the continent before opting for the Bernabeu. He is yet to make his mark with the 13-time European champions and, after being restricted to only three league starts this term, has been loaned out for the fourth time. Arsenal are undoubtedly the highest-profile club he has joined on a temporary basis following spells at Dutch sides Heerenveen and Vitesse Arnhem and in LaLiga with Real Sociedad. He showed plenty of promise during his stay in the Basque region and now has a greater platform to justify the hype which has dominated his fledgling career.