The 22-year-old former Ajax wideman will join the Owls on a three-year contract subject to passing a medical at Hillsborough.
"I am delighted to be able to bring a player of quality from Vitesse Arnhem in Holland," Wednesday boss Brian Laws said.
"Etienne Esajas is quick and moves the ball well, he is a very good crosser and he has impressed me immensely in training so far.
"He still has a year left on his contract but we have successfully agreed a fee with Vitesse and I believe he will be a great acquisition for Sheffield Wednesday and become a crowd favourite."