Jobava has played for the Georgian national team in the Chess Olympiad since 2000. He won the individual gold medal in 2004, scoring 8½/10 points. In 2010, he defeated the world's number one player Magnus Carlsen in the Georgia–Norway match. In 2016, he won the individual gold medal for the best performance, which included wins over the former world champions Ruslan Ponomariov and Veselin Topalov.