"I am 99% sure we will sign the document on January 4," Grigol Vashadze said at a briefing, adding that the text of the agreement was being finalized.
The minister earlier said the agreement would stipulate close political, economic and humanitarian ties, as well as cooperation in the security sphere.
The United States signed a similar deal with Ukraine earlier this month, which along with Georgia is hoping to join NATO. The alliance pledged to boost ties with the two ex-Soviet countries at a ministerial meeting earlier in December, although it did not offer them Membership Action Plans.
Georgian President Mikheil Saakashvili said on Monday: "With the agreement signed Georgia will become stronger and will be able to travel the path to restoring its territorial integrity."
He said that by establishing a strategic partnership "with the biggest and strongest state in the world ... relations will reach a new level of security not only in Georgia, but in the whole region."
Georgia lost control of Abkhazia and South Ossetia in bloody post-Soviet conflicts in the early 1990s. The two republics, bolstered by Russian peacekeepers, have had de facto independence since then, and have been a bone of contention between Georgia and Russia.
Russia recognized Abkhazia and South Ossetia as independent states on August 26, two weeks after a five-day war with Georgia, triggered by Tbilisi's attack on South Ossetia.