Thomas Howard, 25, and Thomas Baty, 26, were travelling with touring side Clems Pirates, who are based in their home city of Durham.
Mr Howard died on Sunday and Mr Baty, who had been critically ill, passed away in hospital today.
They visited a nightclub in Colombo after a match against a local team and complained of breathing difficulties after returning to their hotel.
Post-mortem samples have been sent for further analysis to establish the cause of death.
The squad arrived in Sri Lanka on May 9.
Among the rugby clubs to pay tribute to the pair was Skipton-based Wharfedale, who tweeted:
"Our recent worries are put into perspective when compared to the devastation that must be being felt at Durham City RFC and by all those that knew & loved Tom Baty & Thomas Howard. Our sincerest condolences. #RugbyFamily."