Arteta was confirmed as Arsenal’s new manager on Friday afternoon, becoming Unai Emery’s successor on a three-and-a-half year deal.
The Spaniard said his goodbyes to staff at City on Thursday, having arrived at the club with Guardiola in 2016.
Arteta is the second senior member of coaching staff that Guardiola has lost in the last 18 months, following Domenec Torrent's departure for New York City FC last year.
Torrent has since left his position at New York, but Guardiola confirmed on Friday that City would not make any external appointment to replace Arteta before the end of the season.
“We’ll stay with the same people. Right now we are not adding anyone. We’ll work with the people who are here.”
On Arteta, Guardiola added: “He decided to move there. When you have dreams you cannot stop it. You have to follow your dreams.
“Arsenal was important in his career, one of the best teams in Europe. I wish him all the best – I’m sure he’ll do an excellent job.”
Third-place City welcome second-place Leicester to the Etihad for Saturday's tea-time kick-off, with both sides capable of closing the gap on leaders Liverpool.
Sergio Aguero and John Stones have both taken part in training and are in contention to play, but David Silva is still recovering from a knock sustained in the defeat to Manchester United.