Thomas Howard, 25, was admitted to hospital in the capital Colombo on Sunday after suffering from breathing problems and died soon after, said his club Durham City RFC.
His team-mate Tom Baty, 26, who is thought to be seriously ill, remains in hospital.
A statement on Durham City’s website said: “The club is now in a position to confirm the names of the two members of the touring party that received medical attention in Sri Lanka.
“The deceased is Thomas Howard, 25, from Durham City. He was admitted to hospital in Colombo after suffering breathing problems on Sunday, 13 May.
“Tom Baty, 26 also from Durham City was admitted to hospital in Colombo after suffering breathing problems on Sunday, 13 May and remains in hospital receiving treatment,” it added.
Sri Lanka Police said the players, who toured with Clem Pirates, part of Durham City, complained of breathing difficulties at around 10am and Howard died in hospital two hours later, at noon, local time.
The pair, along with other team-mates, had gone to a nightclub in the capital Colombo and returned in the early hours of Sunday morning.
Police spokesman SP Ruwan Gunasekera said the men were part of a touring team that arrived in the country on Thursday.
He added they were staying at a hotel in Colombo after playing their opening match against Ceylonese Rugby and Football Club on Saturday.
The Foreign Office confirmed it was dealing with the incident: “Our staff are supporting the family of a British man following his death in Sri Lanka, and are in contact with the Sri Lankan hospital services.”
“We are assisting the family of a British man who has been hospitalised in Sri Lanka, and are in contact with the Sri Lankan medical services,” it added.
Local Durham County Councillor Dr David Boyes said Durham City RFC was very well organised and had undertaken numerous tours abroad in the past without problems.
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“I really feel for the families, being that far away and knowing that a family member has died must be terrible,” he said.
Clem’s Pirates tours regularly across Europe and further afield and is well known in the area especially for its fundraising efforts and tours.