The German defender became the frontrunner to take the armband once Arteta joined Pep Guardiola's coaching team at Manchester City at the end of last season.
Mertesacker has been an Arsenal player for the last five years, making 149 appearances, and in that time winning two FA Cups.
However, he will miss the first few months of the new season due to a knee injury.
Manager Arsene Wenger told Arsenal Player: "Per is a very respected figure in the dressing room, is loved as well and is also a very demanding figure. I think it is absolutely natural [for the captain] to be [him].
"[In his absence] that's where it will be taken by the assistants. One of them will be Laurent Koscielny, also Santi Cazorla - the experienced players - Petr Cech maybe.
"We will have a group of people that will take care of the energy levels and the problems of the team. That will be down a lot to the experienced players."
Arsenal will begin their 2016-17 campaign with a clash against Liverpool at the Emirates tomorrow.