The 22-year-old was serving in Malawi as part of an anti-poaching operation and was on patrol in Liwonde National Park when the incident happened, the defence ministry announced last Tuesday.
"He was killed by an elephant," the spokesperson said, explaining that Talbot died later of his injuries.
"This tragic incident is a reminder of the danger our military faces as they protect some of the world's most endangered species," Defence Secretary Penny Mordaunt said in a statement.
The presence of well-equipped British forces in Liwonde park has been reassuring for rangers who routinely confront gangs of poachers armed with Kalashnikovs.
Talbot's commanding officer Ed Launders said he was "determined and big-hearted" and had volunteered for the mission to Malawi.
"He was hugely proud of his work as a counter-poaching operator and tragically died doing great good," Launders said.
Talbot enlisted in 2013 and last year attended a multi-national training exercise in Kenya.