The 29-year-old striker (pictured) is currently without a club after being injured in a pre-season trial stint at QPR.
Webber never made the grade at Old Trafford after emerging through the ranks as a promising youngster, and has accepted an offer from Neil Lennon to head up to Glasgow and prove his fitness.
Released by Portsmouth last season, Webber has also featured for Watford and Sheffield United, and would be able to sign for Celtic immediately given that he is currently a free agent.
The player has recovered from the ankle injury that wrecked his chances of a contract at QPR.
And, if Lennon believes he has something to offer, he could win himself a deal at Parkhead.