The 37-year-old Spaniard, who played more than 100 games for the Gunners between 2011-16, signed a three-and-a-half year contract and ends a three-year stay as Pep Guardiola's assistant at Manchester City.
Arteta, who was officially presented to the press on Friday evening, replaces compatriot Unai Emery, who was sacked last month.
The former midfielder, who will sit in the stands for Saturday's match against another of his former clubs Everton, faces a massive challenge, with Arsenal having won just once in 12 matches, beating West Ham under interim manager Freddie Ljungberg.
"This is a huge honour. Arsenal is one of the biggest clubs in the world," Arteta said in a statement.
"We need to be competing for the top trophies in the game and that's been made very clear to me in my discussions with Stan and Josh Kroenke (owner and club director, respectively) and the senior people from the club.
"We all know there is a lot of work to be done to achieve that but I am confident we'll do it.
"I'm realistic enough to know it won't happen overnight but the current squad has plenty of talent and there is a great pipeline of young players coming through from the academy."
Head of football Raul Sanllehi said the club had interviewed other candidates before opting to pursue Arteta.
"We met several top-class candidates and Mikel stood out to every single one of us as the perfect person for us," he said in a club statement.
"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."
‘Ruthless’
Arteta warned Arsenal's underachieving stars that he will be "ruthless" as he looks to restore a winning mentality to his troubled club.
Arteta arrives at the Emirates Stadium to find a team in crisis following a wretched run that cost Emery his job and reaffirmed the sense the Gunners have lost their way since the final years of Arsene Wenger's reign.
Languishing in 10th place in the Premier League, Arsenal hope Arteta can steady the ship and eventually turn the north Londoners into contenders for a top four berth.
And Arteta made it clear he will take a hardline to ensure the malaise doesn't continue any longer.
"I have to engage the players, when I was here with Man City last week everyone was a bit down," Arteta told reporters.
"We have to have the right culture here, if we don't then the tree will shake.
"After that we can talk about other things. We need an immediate impact and need to raise the level of the performances to start winning games and engage with the fans.
"The ambition of this football club is very clear. You have to fight for trophies and be in Europe. The rest is not good enough."
Arteta has earned praise from Guardiola for the work he did with City's players during their title-winning campaigns.
The Gunners boss is ready to put the lessons he learned from Guardiola into action, starting with a single-minded approach to installing his own philosophy at a club desperately lacking purpose and unity in recent years.
"What I have learned mostly is you have to be ruthless, consistent and fit the culture of the club to sustain a winning mentality," Arteta said.
"Every act is important. Pep's work-rate is incredible. The staff have to be able to transmit it and when the players buy into that, you can be strong.
'Be responsible'
"I want to do things my way by convincing them it is the right way for everybody to live better.
"Everybody has to be responsible and I do not want them hiding, I want people who deliver passion and energy.
"Anyone who does not buy into this, has a negative effect, is not good enough for this environment and culture."
The 37-year-old won the FA Cup twice in a five-year playing career with Arsenal, then joined City to work with Guardiola after retiring in 2016.
He revealed he came very close to taking the Arsenal job following Wenger's departure in 2018, but conceded it was not the right time for him then, whereas now he has the knowledge to make a success of a difficult situation.
Given the huge problems lurking in Arsenal's unbalanced and inconsistent squad, many fans wanted a more experienced boss to replace Emery.
Arteta is adamant he won't be fazed by his first managerial role, saying: "I will give every drop of blood for this football club to make it better.
"I feel back home. I am extremely happy and proud to have been given the honour of being manager of this football club," he said.
"I have prepared for the challenge and am ready. If I didn't feel that, I would not be siting in this chair."
Arsenal haven't won the Premier League since 2004 and appear light years behind champions City and current leaders Liverpool.
One of the main issues facing Arteta is how to deal with German midfielder Mesut Ozil, who has endured testing times of late with Arsenal and is the subject of speculation over a January move.
Pierre-Emerick Aubameyang, Arsenal's leading scorer, is also said to be unsettled by the team's struggles and Arteta wants to get to know those two and the rest of the squad as soon as possible.
"I want to understand how they are feeling and what they need," he said.
"Then I can take the excuses out of them and focus on the things which are relevant on and off the pitch. It is my job to get the best out of him (Ozil)."