The 20-year-old is officially out of contract following the expiry of his Sheffield Wednesday deal at midnight.
Last season was a breakthrough one for the centre-back, making 17 appearances between January and the end of the season.
His performances for the struggling Owls attracted interest from around Europe, including Belgium and Portugal.
The Parkhead club are yet to make a signing since the arrival of Ange Postecoglou.
The Australian spoke of the “urgency” for reinforcements in some positions ahead of the club's Champions League qualifier with FC Midtjylland.
Urhoghide can play centre-back or right-back, positions which require strengthening at Celtic.
Meanwhile, the club today confirmed a new contract for striker Leigh Griffiths.
The forward’s deal had expired but he has penned a one-year extension.