The 23-year-old centre-back will be out of contract with Vitesse this summer and several clubs have been monitoring his situation for a while.
Rangers wanted to sign him in January, but the Dutch club blocked a move and they have been interested in snapping him up on a free transfer this summer.
But Union Berlin have had their noses ahead in the race to sign the defender and Vitesse have confirmed that he is to join Union Berlin.
Doekhi has signed a three-year contract with Union Berlin and will be joining them on a free transfer.
The German club managed to qualify for the Europa League on the last day of the season and that may have played a key role in convincing the player.
The defender will soon be on his way to Germany to complete the formalities of the transfer.
Rangers were interested in signing him but will now have to focus on other targets in the market.
The Scottish giants can offer Champions League football to prospective signings if they win the Europa League on Wednesday night in Seville.
