Raul Sanllehi, the club's head of football, said Arteta "understands" the club and stood out among several top candidates.
"We met several top-class candidates and Mikel stood out to every single one of us as the perfect person for us," said Sanllehi. "Mikel understands Arsenal Football Club and what it means to our fans around the world. We look forward to him getting down to work and bringing the best out of our squad as we work to get our season back on track."
Arsenal are currently 10th in the Premier League table having won just once in their last 12 games. Freddie Ljungberg, the interim head coach, will remain in charge for Sunday's trip to Merseyside to face Everton.
"We're delighted to be bringing Mikel back to Arsenal," said Josh Kroenke, the son of owner Stan. "He knows our expectations and those of our fans around the world are high and we are confident he can play a lead role in taking the club back to the levels we all demand.
"I also want to thank Freddie Ljungberg for skilfully guiding us through the last three weeks. He stepped up at short notice and has helped us through this difficult period with great professionalism."
The 37-year-old's appointment comes as the club confronts another defensive injury crisis, with Sead Kolasinac ruled out until January with an ankle injury he sustained against Manchester City last weekend.
Hector Bellerin is also struggling with a tight hamstring, while Kieran Tierney will be out until March after dislocating his right shoulder in a recent victory over West Ham United.
Teenage winger Bukayo Saka may have to play left-back against Everton, if Ljungberg decides against moving Ainsley Maitland-Niles from right-back. There are also doubts over the fitness of Mesut Ozil, who picked up a foot injury in the defeat by City.
Arteta has already been backed by Unai Emery, who was sacked as Arsenal's head coach last month.
"He really is prepared to make that next jump," Emery told the BBC. "He has been at Arsenal before, he's been in the Premier League and he has been working with Pep Guardiola. I do believe this is a good decision and I would also like it to be a good decision."
Emery also spoke about his struggles this season, saying he "suffered" as the campaign derailed following a promising start.
"When a coach doesn't win, he suffers," Emery said. "And when he doesn't win two, or three or four he suffers more. We had to win to regain our emotional equilibrium, to get rid of that frustration and we couldn't.
"And what is true is the social mass of Arsenal, which is very big, couldn't see it, couldn't connect with what was happening and it is true that in this situation, as happens in every country and with every team, the coach finds himself targeted.
"I spoke to the players three or four weeks before the process began to tell them that things were not going well and that I couldn't see the team I pictured on the field of play, I couldn't identify what I was looking for. We looked for solutions but results still didn't come.
"The club made its decision and that was passed on to me by Raul Sanllehi with much regret because he also felt his share of the responsibility and we were very united. But the situation had become unsustainable as regards to the protests of a section of the fans.
"That said, I believe there was another important section who believed we could have been shown more patience and carried on with the project. I think we could have turned things around but I also understand those at the top have to take decisions and take responsibility."
