Root, whose next assignment is the four-Test series India starting February 5, also became the fourth-highest run-getter in Test cricket for England and the first ever captain to hit two double-hundreds.
Ahead of the series starting February 5 in Chennai, Root has described India as "the best team of the world in their own conditions".
Root was the second-highest run-getter behind Virat Kohli the last time England toured India, in 2016-17. His 491 runs in five Tests at 49.1 was behind Kohli's 655.
With the 2-0 win, England are now the most successful visiting team in Sri Lanka and have equalled India's tally for most matches won by a visiting team in Sri Lanka.
After notching up a double century in the series opener, Root continued his brilliant run by hitting 186 in the second Test to lift his side from a spot of bother.
The right-handed batsman has amassed 8,238 Test runs in 180 innings he has played so far and is fourth on the list of leading run-getters for England
England skipper Joe Root continued his mastery over spinners on the sub-continent, reaching a second consecutive hundred and helping the tourists reach a dominant total on third day of the second Test at Galle. Root also passed Kevin Pietersen’s tally to become England’s fifth highest run getter.
Root, who had posted his 19th career test hundred before lunch, also passed Kevin Pietersen’s tally of 8,181 test runs to become England’s fifth highest run getter in the five-day format.
Former England captain Alastair Cook is the all-time highest run-getter for England.
The teams are expected to reach Chennai by January 27 and undergo testing before entering the bio-bubble.
An injury-hit India, who were also missing some star players like skipper Virat Kohli, registered a three-wicket win in the series-deciding fourth Test against Australia.
Resuming on 38/3 on Day Five, wicketkeeper-batsman Jonny Bairstow and debutant Danial Lawrence carried England to their 76-run target inside 35 minutes on the final morning of the Test match.
Root’s 228 had provided England a strong total of 421 and a meaningful first innings lead of 286, but Thirimanne stood firm for two sessions to remain unbeaten on 76 off 189 balls and carried Sri Lanka to 156-2 at stumps.
Root ended his long wait for a hundred with the addition of an 18th Test century to his name and later converted it to a well-composed 228 off 321 balls laced with 18 fours and a six in England's first Test against Sri Lanka at the Galle.
England resumed at the overnight score of 127 for two and lost the wicket of Jonny Bairstow early with the addition of just four runs.
England are embarking on a three-month tour of the subcontinent, starting with two Tests in Sri Lanka, which were supposed to be held last March and followed by a full-fledged series in India.
England had curtailed their tour of South Africa recently with the ODI series being called following some positive cases among South African players.
While Joe Root called Virat Kohli 'most complete player' across formats, he named teammate Jos Buttler as the most complete white-ball batsman.
Joe Root has said that he is determined to make a comeback to the England T20I side ahead of the 2021 World Cup in India.
According to Yorkshire Cricket's official website, Root has asked the England management to allow him to get some game time in T20 cricket, a format he is not an automatic choice for in international cricket.
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