The 25-year-old, who can play at right-back or in the centre of defence, agreed a three-and-a-half-year contract in November after leaving Norwegian side Rosenborg.
Lustig watched Celtic go top of the SPL table with Wednesday's defeat of Rangers and could make his debut in Monday's match at Dunfermline.
A statement on www.celticfc.net read: "Celtic Football Club are delighted to confirm that new Bhoy Mikael Lustig has passed his medical and confirmed his new deal.
"The Swedish international, who signed a pre-contract earlier in the season, has been in Glasgow over the past few days to take in the derby victory and finalise his new contract - which will officially start on January 1, 2012.
"Mikael will be officially unveiled as a Celt at a media conference at Lennoxtown [on Friday]."
Lustig's arrival strengthens the Swedish connection at Celtic, whose record goalscorer is Henrik Larsson.
Johan Mjallby was a successful defender for the club and is now manager Neil Lennon's assistant, Daniel Majstorovic is a key figure in the defence and Freddie Ljungberg had a short spell at Parkhead last season.
Lustig will rival Adam Matthews, Cha Du-ri and Mark Wilson for the right-back berth.
Source: PA
Source: PA