The 19-year-old is versatile and can play anywhere across the back line.
While he was highly rated at youth level, he never made the step up to United's senior team.
He will now sign for Celtic in a permanent transfer, with the deal closing before the European transfer window shut on September 2.
O'Connor has been at Manchester United since 2016 and played for their under-23 team as recently as last week.
Many were surprised he was released permanently, but it is possible United included a buy-back clause in the deal.