The 24-year-old Yorkshireman hit 130 in the first innings at Trent Bridge as England won by an innings and 78 runs.
Root has scored 443 runs at an average of 71.79 so far in the series with two centuries and two half-centuries.
He replaces Australia's Steve Smith, who slips to third in the rankings with South Africa's AB de Villiers second.
Root is the sixth England player to top the batting or bowling world rankings since 1980.
He made his Test debut against India in December 2012 and has scored 2,716 runs in 31 matches at an average of 56.58
Speaking after England regained the Ashes, Root said: "I put my form down to hard work, being very relentless in your practice, and doing the things you don't want to - you've got to face bowling in practice that whistles around your head."
Meanwhile, England's Stuart Broad has moved up three places to second in the bowling rankings after taking 8-15 in the first innings at Nottingham.
James Anderson is third after missing the fourth Test with a side strain, while South Africa's Dale Steyn remains top of the rankings.
Joe Root has become the leading batsman in the ICC world rankings after helping England beat Australia to regain the Ashes on Saturday.