Engineer Technician Charles Warrender, 23, from North Thoresby, Lincolnshire, was found dead in the capital Victoria on Saturday morning.
He was serving on Portsmouth-based ship HMS Richmond, which is part of Operation Kipion in the Indian Ocean.
A navy spokesman said next of kin had been informed but declined to comment further while inquiries continued.
Mr Warrender, whose body was discovered behind the national library, had been living in Portsmouth.
HMS Richmond, a Type 23 frigate, had hosted a reception on board for British High Commissioner Lindsay Skoll last Friday to mark the Queen's birthday.
A statement from Mr Warrender's family said: "Charlie was a charismatic and loving young man, who made everyone who met him smile.
"He was extremely proud to serve in the Royal Navy and was thoroughly enjoying travelling the world, progressing his career as a Marine Engineer.
"Charlie's family are all very proud of him and he will always be remembered as a funny, loyal, and kind son, brother, partner and friend."
The death of a Royal Navy sailor during an operation in the Seychelles is being investigated by police.