Gullit awarded his compatriot the distinguished accolade and feels the 28-year-old is essential to any plans Arsenal manager Arsene Wenger has to break the Gunners' eight-year wait for silverware.
"Yes he is vital to success," Gullit told Press Association Sport.
"Arsenal need to win trophies and I think Van Persie wants to and he knows if he wants to become one of the legends of football he needs to win trophies and he will ask Arsene Wenger to strengthen the squad. The team need to give him help."
Two-time European Cup winner Gullit has been very impressed with the performances that earned Van Persie the player of the year award and seen him score 27 league goals this season to date.
"He has been unbelievable," he said. "I think he has shown people what he is capable of both in the manner of style and grace and he is also the leader of the team and that is what impresses me even more."
Former Arsenal forward Alan Smith echoed the opinions of Gullit and believes the Gunners' skipper has done a great job in changing the way he plays.
"He is a class act and I can't see any reason why he can't score many more goals, if Arsenal can keep hold of him of course - which they really need to do," he said.
"I think if you're playing as an out-an-out striker rather than a classic number 10, which is what he is naturally, you are going to get into more goalscoring opportunities but that is the impressive thing from Robin's point of view the way he has adapted his game.
"The runs he has learned to make on the back of defenders is amazing really, he plays like an orthodox striker now."
The Holland international beat Manchester City midfielder David Silva and Manchester United striker Wayne Rooney into second and third places respectively after the latter had suggested earlier in the week that Van Persie was his choice for the trophy.