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Ketsbaia stepped down from the role in November after a 4-0 loss to Poland in Euro 2016 qualifying, in which they have accrued three points in four Group D games.
Tskhadadze, a former national captain, signed on for two-and-a-half years to lead the 125th-ranked country.
"I trust the lads and want to tell them they're great and capable of winning and qualifying for major tournaments," Tskhadadze said.
"Being head of your national team is the biggest job you can get as a coach, a dream for anyone.
"I'm glad I'll have a chance to contribute to football's development in my country."
Tskhadadze's first competitive charge could not be a tougher challenge - as Georgia host World Cup winners Germany on March 29 in their next Euro qualifier.
The 46-year-old will continue to juggle duties with Georgia and Azerbaijani title contenders Inter Baku - who were involved in the UEFA Europa League this term - until June.
