Both reported breathing difficulties after leaving a nightclub in the city early on Sunday morning.
The players, both from Durham, were on tour with one of the club's teams, the Clems Pirates.
They were admitted to hospital after they started suffering from breathing problems.
Durham City Rugby Club, which oversees rugby union "veterans" team the Pirates, said in a statement the pair suffered "non-rugby related breathing problems" and were admitted to hospital.
"A further statement will be issued in due course".
He is the second Durham City Rugby Football Club player to die in just two days after Thomas Howard, 25, passed away on Sunday afternooon.
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The membership confirmed with "nice disappointment" that Baty, his 26-year-old teammate had additionally died Tuesday.
A British rugby player has died in Sri Lanka after returning from a night out - with a team-mate left in critical condition.
In a statement released on Tuesday, the club requested that the privacy of their families be "respected and upheld at this hard time".
The two players complained of breathing difficulties to the hotel management at about 10am on Sunday.
"We would also like to take this opportunity to thank everyone for the many messages of sympathy and support that have been received from our members, friends and the wider rugby family; they are very much appreciated at this hard time".
A British High Commission spokesman in Colombo said both families were being supported, and they were in contact with the Sri Lankan medical services.