The forward could make his second debut for the club this weekend against Reading if he gets international clearance.
Both manager Neil Lennon and Gudjohnsen had confirmed the former Chelsea and Barcelona forward was training with the club recently.
Lennon told the BBC earlier in the week: !I think he'll be a big-game player and enjoy the occasion. It will take him a little bit of time to adjust to the Championship and the quality of player he's used to playing with.
"We need that type of player with Mark Davies out and Chung Yong-Lee might not be here [because of international commitments] in January."
The 36-year-old has enjoyed a glittering career having won the Premier League twice with Chelsea, the Champions League with Barcelona amongst a long list of major honours.
The Icelandic forward will wear the number 22 shirt, according to the club's website.
Former Premier League striker Emile Heskey, who is currently a free agent, has also been linked with a move to the Macron Stadium.