Sterling has moved to Rotterdam as a free agent after securing a release from his contract at Chelsea last month.
The winger has penned an initial deal to the end of the season.
Van Persie said: "It is of course fantastic that after closing the transfer window we managed to tie another player of the calibre of Raheem.
"His football CV speaks for itself: he is a player whose qualities can absolutely make a difference in a match and I am convinced that he will help us in the last half of the season to achieve our goals."
Meanwhile, Sterling also remarked: "Because of my transfer-free status, I had the opportunity to take the next step in my career for the first time in a long time. I took my time to do that and talked to several clubs and their head coaches. This is to understand what role they had in mind for me and to make sure that I can really be an added value at a new club.
"After talking very extensively with Dennis (te Klose, sporting director) and with Robin, I am convinced that Feyenoord is the place where I will be happy and also a valuable member of the selection.
"Playing abroad is a whole new challenge for me – and one that I like to embrace. I'm really excited to get started. To Feyenoord and in particular Robin and Dennis: thank you for your patience and professionalism as I went through this process."