Kohli surpassed the earlier record of batting legend Rahul Dravid who scored 619 runs from eight innings in the 2003-04 tour of Australia.
The 26-year-old Kohli, who came into this match with an aggregate of 499 runs, has now totalled 639 from seven innings.
Kohli, who struck his fourth ton of the series and 10th overall in his 33rd Test, is now the only cricketer ever to have scored a century each in his first three innings as captain of a side. Australian Greg Chappell had scored a century each in his first two innings as skipper against the West Indies at Brisbane in 1975.
He also became the first Indian batsman after Sunil Gavaskar (in 1971 and 1978-79 versus West Indies) to score four centuries in a Test series.
The feisty batsman, who made his Test debut in 2011 against the West Indies, also became the first overseas batsman since Herbert Sutcliffe (1924-25) and Walter Hammond (1928-29) to score four hundreds in a Test series in Australia.
PTI