The France striker suffered a damaged left tibia in a 2-2 Premier League draw at Everton back in August and underwent surgery four days later.
Giroud was expected to return at the end of December, but Arsenal manager Arsene Wenger last month revealed that the former Montpellier frontman was ahead of schedule with his rehabilitation.
And the 28-year-old was able to participate in a full training session with the London club on Thursday as he closes in on a return.
Wenger has had to contend with long-term injuries to Mesut Ozil, Mathieu Debuchy and Laurent Koscielny this season, while Theo Walcott has not yet started a game since his comeback following a serious knee injury.
Danny Welbeck has led the line in the absence of Giroud, while Alexis Sanchez has been prolific since his move from Barcelona but Wenger has limited attacking options in his squad so Giroud's return to fitness will be a major plus.
Arsenal were in need of a lift after suffering a 2-1 Premier League defeat at Swansea City on Sunday following a dramatic 3-3 draw against Anderlecht in the UEFA Champions League which saw them squander a three-goal lead.
