The 22-year-old full-back signed a five-year contract after personal terms were finalised today.
Kieran Tierney is already the most expensive player in the history of Scottish football.
The Celtic left-back just completed an English transfer deadline day move to Arsenal for a fee of around £25m.
Tierney, 22, signed a deal with the Premier League giants after travelling to London on Wednesday.
The three-time PFA Scotland Young Player of the Year joined Celtic at at the age of just seven and rose through the youth ranks to become a vital player at club and international level for Scotland.
Injury problems meant he didn’t feature in any of Celtic’s five Champions League qualifying games over the last month.