The former Hearts player had stayed in England awaiting the birth of his first child as his international team-mates met on Monday to prepare for Saturday's opening World Cup qualifier against Serbia.
Scotland manager Craig Levein said: "On behalf of the squad we are delighted with the news and send our congratulations to Christophe and his family.
"We look forward to him joining up tomorrow. He has been training at his club this week so there are no issues with him fitness-wise and I am sure he will come up on a high.
"Christophe is a very important player for us and it will be good to have him available for Saturday."
The centre-back is now almost certain to play, giving manager Levein some welcome good news on the defensive front.
Levein was already without full-backs Steven Whittaker and Phil Bardsley and saw Danny Fox and Russell Martin pull out on Monday, while Celtic's Charlie Mulgrew is receiving treatment for an Achilles knock.
Levein called up Huddersfield left-back Paul Dixon and MK Dons defender Gary MacKenzie on Monday.