The 21-year-old Japanese midfielder is set for his fourth spell at another club since signing for Arsenal, following Ignasi Miquel out of the door on transfer deadline day.
The 21-year-old's move marks a return to Dutch football, having spent the second half of the 2010-11 season on loan at Feyenoord.
Last season was the first of Miyaichi's career with the Gunners that he did not go out on loan but the youngster made only seven appearances in all competitions for Arsene Wenger's side.
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He has also previously spent time representing Bolton and Wigan but has yet to make an impression on his parent club's first team.
Miyaichi is the second player to leave the Emirates Stadium on transfer deadline day, with Ignasi Miquel having joined Norwich City on a permanent deal.