The 34-year-old also confirmed his retirement from playing after a five-year stint with the Gunners, during which time he won two FA Cups.
The former Everton and Rangers midfielder, who started his career at Barcelona, has been a rumoured target of Guardiola since the Spaniard's appointment as City boss in February.
"Following recent media speculation surrounding my future I can confirm that I will be leaving Arsenal and retiring from playing to take up a coaching position at Manchester City," Arteta wrote on Twitter.
"I've enjoyed an amazing five years at Arsenal and it's been an honour and a privilege to captain such a great club.
"I am now looking forward to the challenge ahead at Manchester City
The opportunity to join Pep Guardiola and his team was an amazing opportunity for me and I am incredibly excited for the future."
Arteta thanked Arsenal boss Arsene Wenger, his team-mates and the supporters, while reflecting on a memorable spell in north London.
The path from the Emirates Stadium to the Etihad Stadium is a well-worn one, with Arteta following Kolo Toure, Emmanuel Adebayor, Bacary Sagna, Gael Clichy and Samir Nasri to Manchester.
Patrick Vieira, another former Gunners captain, also began his coaching career at City
The Frenchman is now boss of New York City FC, who are owned by Manchester City.
Arteta says he has long considered a coaching role and aims to be part of a successful group at City.
"Throughout my career I have always been interested in more than just the playing side and have had a passion for helping progress and develop the team outside of just my own role as a player," added Arteta, who has been troubled by injuries in recent seasons.
"Coaching has always been something I've been keen to go in to and over the past few years I've worked hard off the pitch as well as on it to develop my skills in order to put me in a position to be able to pursue a coaching role once I finished playing.
"I have been lucky enough to play under some amazing coaches and managers during my playing career and I hope to use elements of everything I've learnt from them as well as experience from my own playing career to help City achieve success."