The 23-year-old takes over the role after Alexandre Lacazette's departure to Olympique Lyon this summer left the armband vacant.
Lacazette himself had assumed the role temporarily after Pierre-Emerick Aubameyang was stripped of it for disciplinary reasons last December and subsequently sold to Barcelona.
Odegaard joined Arsenal initially on loan from Real Madrid in January 2021 and the move was made permanent for £30m at the start of the 2021/2022 season.
There were a number of other candidates for the role, including Kieran Tierney, Aaron Ramsdale and Granit Xhaka but Arteta has settled on Odegaard, who also captains the Norway national team.
Arsenal made the announcement concerning their captaincy prior to Saturday afternoon's Emirates Cup game against Sevilla.
A statement on the club's website read: "We are delighted to announce that Martin Odegaard has been named our new men’s first-team captain.
"The 23-year-old has made a huge impact since arriving at Emirates Stadium from Real Madrid in January 2021, initially on loan, and has gone on to play 60 times and scoring nine goals.
"Odegaard has experience of wearing the armband, having been Norway captain since March 2021, whom he has won 43 caps for.
"We wish Martin every success as our captain.We will have more on the appointment here after today's match."
Arsenal start their season away at Crystal Palace in the Premier League next Friday.
