The former United goalkeeper played a vital role in negotiating van de Beek's arrival at Old Trafford.
Taking out an open letter in the Manchester Evening News, van de San wrote: "Dear Manchester United fans
"I hope you're doing well.
"It seems our paths have crossed again. One of ours is joining you this season. And like so many players before him, he's been with us since he was just a little boy.
"Shortly after his debut, he became one of our best. Especially the last couple of years were amazing. From the Europa League final (no hard feelings) to our Champions League run and winning the Dutch Championship.
"The team he was part of the showed the world who we are and what Ajax stands for.
"Like you, we pride ourselves on being one of the best at developing talent and giving young players a shot at the highest level. You could say your new star is the embodiment of that pride.
"That's one of the many reasons we don't like to see him leave, but we understand it's time for him to move on. To dream on.
"And where better to do so than in your theatre. Trust me, I know.
"Please take good care of our Donny, and help him dream.
"Enjoy the future."
Enjoy the Future. #DreamLikeDonnypic.twitter.com/QVKS3Q0Snk
— Edwin van der Sar (@vdsar1970) September 3, 2020