The 22-year-old fleet-footed winger joins on a three-year deal on an undisclosed fee from the Eredivisie outfit and is set to be part of the squad for the game with Bristol City on Saturday, subject to international clearance.
Esajas came through the famous Ajax youth system and has already trained with his new team-mates subject to the move being completed today.
He told the club's official site: "I have been with Vitesse Arnhem for two seasons and my manager called me to ask if I wanted to go on trial in England. I thought 'why not?' because it is Sheffield Wednesday, it's a big club and I think they should be in the Premier League."
Esajas will wear the number 11 shirt vacated by Chris Brunt who joined West Brom recently and watched the game at Hillsborough last night.
Meanwhile, Brian Laws praised his troops after a hard-fought win over Hartlepool last night.
Yoann Folly's last-minute goal in extra time was enough to see Wednesday through to the next round, which is drawn on Saturday.
Laws said: "I am delighted with the response we had from the players - this isn't an easy game. Hartlepool would have been coming here thinking 'look at Wednesday, they're struggling, conceding goals for fun'.
"This was a big test for us yet the win was deserved."