The Swiss defender was in Glasgow for talks on Friday and the transfer went through in time for him to play against Aberdeen this weekend.
The 29-year-old has joined the Scottish giants at the perfect time - Martin O'Neill's men are currently seven points clear at the top of the Scottish Premier League.
Boss O'Neill told Celtic's official website: "We are basically taking his contract over and then what he does is really up to him.
"But he is free to speak to anyone he wants in January and it is the little period before Christmas that is important to us.
"Then, after the break, we will take it on from there. But I just wanted a few extra people around."
Vega joined us from Italian Serie A side Cagliari in January 1997 but his time at the Lane has been wrecked by injuries.
Indeed, after arguably his best game in a Spurs shirt to help us lift the Worthington Cup in March 1999, a broken foot followed by a series of ankle problems ruled him out until this summer.
Vega enjoyed a nine-game run in the side earlier in the season but has recently lost his place to the emerging talent of Alton Thelwell.
He recently hinted that he might have to move on in his last interview as a Spurs player. Read that story by clicking here
Ramon Vega has completed his move to Celtic.