The 28-year-old Hungary international moved to The Lions Den in January on a short-term deal under former manager Richard Gough.
Boss Paul Lambert said: "Gabor is a key man for this season. This is like signing a new player.
"He returned to Hungary a few days ago to sort out his affairs and we are delighted that he is now free to renew his connection with Livingston."
Vincze arrived in Scotland in January along with countrymen Ferenc Horvath and that big diddy also known as Attila Kriston, who have both since moved on.
"While he has been unable to play, he has been in training with us since our pre-season trip to Italy," added Lambert.
"He should be available for selection for our first home game on Saturday."