Wilson Officially Signs For Celtic
'We have agreed the fee with Celtic and Mark passed his medical this morning,' said United chairman Eddie Thompson.
Wilson, 21, has been tracked by Celtic boss Gordon Strachan for some time and is the club's first signing of this month's transfer window.
Although the Parkhead side are seven points clear at the top of the Scottish Premier League, Strachan has admitted concern over the frailty of his defence in recent games.
Thompson was resigned about losing one of his club's prized assets.
'We didn't want to lose him but he had a clause in his contract stating that, if a club met the agreed asking price, he could go,' he said.
'We were faced with the possibility of him leaving on a pre-contract last season so at least this way the club has got something back.'