The two centres join Cardiff Metropolitan University as testing facilities for players reported in international cricket under the ICC regulations for the review of bowlers reported for chucking, the ICC said in a media release.
The two facilities were assessed against a range of criteria, including having an indoor area large enough to allow a player to bowl off his or her normal full run-up.
The ICC has provided its testing protocol, which includes a suite of testing equipment and software, to the three accredited centres, to allow for a consistent assessment of bowlers across the different facilities and countries.
ICC General Manager - Cricket, Geoff Allardice said: "We are pleased to announce the accreditation of these two new testing centres, which will help us better manage the issue of illegal bowling actions in cricket."
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"The facilities also allow for bowlers in domestic competitions and in under-age squads to be tested against the ICC standard before they represent their country," he added.
The accreditation of the National Cricket Centre and the Sri Ramachandra University is part of an ICC effort to tackle the issue of illegal bowling actions in a number of ways, including the location of accredited testing facilities in each region.