The midfielder made 12 appearances for the Trotters last season as they were relegated from the Premier League, and believes the experience will help his progression
The 19-year-old was a surprise capture for the Gunners when they signed him in 2010 straight from his high-school team, despite the fact he had not featured in the J-League.
Miyaichi has since impressed while on loan at Dutch side Feyenoord and Bolton, and the winger has expressed his delight at finally being back in north London before setting his sight on continuing his progression.
"I'm very happy to be at one of the biggest clubs in the world," he told ESPNStar.com.
"Now I have to keep working hard.
"When I came in my first year, it was a big surprise for me suddenly seeing a lot of famous players at training.
"I had to get used to it and now I'm enjoying every day. I am able to learn from every player in training because they're all big names here at Arsenal."
Miyaichi also believes that his six-month loan spell at the Reebok Stadium was a beneficial experience, and is open to the possibility of plying his trade away from the Emirates in the coming campaign.
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"My loan spell was good for me as it allowed me to play regularly in the Premier League," he continued.
"It was a great experience and helped me.
"I don't know [if I'll be staying at Arsenal or going out on loan] yet. I will have to discuss with the coaching staff and see what happens."
Miyaichi is currently with the Arsenal squad on their tour of Asia, where he is a fan favourite.
And the youngster believes that improvements in Asian football means that foreign players can prosper in the Premier League.
"It is definitely difficult to play in the Premier League but if they work hard, they can definitely achieve something,” he added.
"I think Asian football is definitely on the rise. There are now a lot of Asian players in Europe and the level is getting higher."
Miyaichi will be one of just two Japanese players in England's top-flight next season, following Shinji Kagawa's switch from German champions Borussia Dortmund to Manchester United.
And the youngster believes that the new Old Trafford arrival will be a success in England, adding: "I think he will be able to perform in the Premier League. He's going to be a big player for his team."