Arteta came on as a substitute in the 2-1 FA Cup defeat by Birmingham on Sunday.
“I am thrilled to be back,” Arteta told the club’s official website. “I had a really nice welcome back from the fans and everyone at Goodison so thank you to everyone.
“Today is a day I will certainly remember for a long time. It is a shame about the result, but personally for me it is a really happy day.
“It was a moment I have been dreaming of for months and hopefully I am now back. I am so glad to have the support from the fans and be back playing for Everton.
“I don’t really want to forget the last 11 months because I have learnt a lot from what has happened.
“Injuries are a part of football, but obviously I prefer the good memories in my career.”
He added: “I think we have got a really good squad and when we get everybody fit I think we can compete with any team out there.
“I am feeling good after my return and I am buzzing. I just want to keep myself fit now and keep doing the right things everyday in training.”