Gambhir, who was ranked third before the chart was updated, moved up two rungs after Sangakkara, who was leading the chart, failed to fire in the first Test against New Zealand at Galle.
Clarke could have benefitted from Sangakkara's loss but the Australian vice-captain's disappointing show in the fifth and final Ashes Test at The Oval has opened the door for Gambhir, who returned to the number one spot.
Sangakkara, who had been top prior to the Galle Test, scored eight and 46 in the match, which was not enough to keep him at the top. Clarke could only manage a total of three runs in the Oval Test, a disappointing return for him and one that drops him three places to fifth in the ICC Player Rankings for Test batsmen.
Gambhir became the top ranked batsman in July this year. For Ashes winning England side, off-spinner Graeme Swann has jumped 17 places and into the top 10 in the ICC Player Rankings for Test bowlers for the first time in his career.
The 30-year-old took eight wickets in the match underlying his position as England's top slow bowler and moving to 10th in the latest rankings.
Another England bowler to make an upward move is man of the match Stuart Broad, whose inspired five-wicket haul in the first innings set up the victory for the home team as Australia collapsed to 160 all out.
Broad gains 11 places to 13th spot in the rankings, level with Australia's fast bowler Peter Siddle, who moves up four places after another consistent performance from the 24-year-old Victorian.
The bowling list is still headed by South Africa's Dale Steyn with Muttiah Muralitharan of Sri Lanka second and Australia's Mitchell Johnson hanging on to third.
Harbhajan Singh (5th) and Zaheer Khan (8th) are the two Indian bowlers in the top 10 chart.
Former Sri Lanka captain Mahela Jayawardena has moved up two places to seventh in the batting list following his first-innings century against New Zealand.
Australia's Ricky Ponting may have scored a battling half-century in the second innings but his overall match contribution did not save him from losing two places as he slips to ninth in the rankings.
Victorious captain Andrew Strauss was the stand-out England batsman of the series and his two half-centuries at the Oval were enough to move him up three spots to 12th position, level with South Africa's AB de Villiers.
