Van Persie, 41, joins from Heerenveen, who he took charge of last May in his first senior managerial role.
The Netherlands' all-time leading scorer went into coaching after retiring in 2019 and he has previously worked with Feyenoord's youth sides.
It's bound to be an emotional return to De Kuip for Robin, as he began and ended his playing career with the Rotterdam giants, who qualified for the Champions League's last-16 on Tuesday, overcoming AC Milan 2-1 on aggregate.
Pascal Bosschart has been in interim charge of the side since they parted company with Brian Priske earlier this month.