Rear Admiral Sinniah, who played a decisive role in the destruction of the LTTE warships in deep sea during the height of the civil war, was appointed as the Navy chief by President Maithripala Sirisena.
"Rear Admiral Travis Sinniah, who has served Sri Lanka Navy with immense loyalty for many decades, took office as the Navy Commander today," President Sirisena tweeted.
His services will be effective from August 22. Rear Admiral Sinniah succeeds Vice Admiral Ravi Wijegunaratne who has retired.
He is the second Tamil to head the Lankan Navy after Rajan Kadirgamar, who was the commander in the late 1960s.
Rear Admiral Sinniah is the first from the Tamil community to head the Navy since the outbreak of the civil war in the north and east of the island in 1972.
He successfully commanded a mission in 2007 to destroy the LTTE's weapons smuggling ships in international waters off Indonesia and Australia, that is considered as Sri Lankan Navy's biggest achievement, media reports said.
Rear Admiral Sinniah, who joined the Navy in 1982, was the senior most Naval officer to be in active combat operations at sea during the conflict with the LTTE separatists.
It was also announced that Vice Admiral Wijegunaratne would be appointed as the Chief of Defence Staff (CDS).
The LTTE waged a war with the government to carve out a separate Tamil homeland in the regions with the conflict ending in 2009. Tamils in the country claim discrimination at the hands of the Sinhala majority.
According to UN figures, up to 40,000 civilians were killed by security forces during Rajapaksa's regime that brought an end to the brutal civil war with with the defeat of Liberation Tigers of Tamil Eelam (LTTE) in 2009.