After starring for Shamrock Rovers in their Europa Conference exit to FC Flora Tallin, a tie in which the 23-year-old scored, he will now move to the Hoops who made it through to the group stage of the Europa League on Thursday night.
Manager Ange Postecoglou told the club website: “Liam is a young player who has impressed us and is someone who we think has the potential to have a big future at Celtic. He is an athletic defender who has the ability to play in a number of positions.
“As I have said before, everyone at the club has been working hard to add depth and quality to our squad and in signing Liam I think again we have made good progress. We all look forward to welcoming Liam to Celtic and to start working with him."
Scales has been with the Dublin club for two years and earned Republic of Ireland under-21 recognition.
A deal, suggested to be in the region of half a million pounds has been necessary to secure the defender ahead of the transfer window closing. Celtic are keen to add to their squad with Ange Postecoglou believed to be seeking a defender, midfielder and another striker ahead of Tuesdays deadline.
Greek forward Giorgos Giakoumakis, the leading scorer in Holland's Eredivisie last season, is another on the Parkhead radar, though negotiations are said to have hit a stumbling block.