Emergency crews were called to the Radisson Blu hotel at around 10:30pm on Thursday.
Norway police said on Twitter there was "no crime" suspected in either case and were not treating the deaths as suspicious.
While, tournament spokesman Jarle Heitmann said both died of natural causes.
"We regard these as tragic but natural deaths. When so many people are gathered for such a long time, these things can happen," he said.
Mr Heitmann said there was a brief moment of panic as emergency workers rushed to attend to the Seychelles player, as some participants apparently mistook their defibrillator for a gun and fled toward the exits.
Former Australian chess grandmaster Ian Rogers, retired from chess in 2007, after he was warned by his doctors that the stress of top-level competition was causing him serious health problems.
The tournament had 1,800 competitors from 174 countries, accompanied by more than 1,000 coaches, delegates and fans.
China won the men's title and Russia won the women's title in the biennial chess tournament in which about 3,000 people participated.
- Daily Mail