The other team members - Kate French, Joe Choong and Jamie Cooke - will be making their Olympic debuts.
Modern pentathlon is made up of five disciplines: swimming, horse riding, fencing, shooting and running.
Find out how to get into modern pentathlon with our special guide.
Murray said it was her goal to become the first British female pentathlete to win medals at two Olympic Games.
"The Olympic Games means everything to me. Having competed at London I now know what it's all about, I know what it's like to compete at the Games and I feel like I know what it takes to get on the podium again," she said.

The 31-year-old comes in as a replacement for Danny Ward, who was recalled from his spell at Pittodrie by parent club Liverpool this week.
Collin, who joined Rotherham from Carlisle United in 2013, has played twice this season.
But he has not featured since August and recently found himself relegated to third choice.
Aberdeen manager Derek McInnes hopes to have Ward available to face Ross County in their Scottish Premiership game in Dingwall.
"We're still waiting for international clearance for Adam and I'll announce the team on Sunday morning," he said.
"We'd assurances from Liverpool that Danny could stay, but their circumstances changed, so we're delighted to get Adam on board."
Ward impressed during his spell with the Dons and, on his return to Anfield, was immediately handed a place on the bench for the game against Arsenal.
There had been suggestions that Aberdeen would consider recalling Danny Rogers from his loan with Falkirk and the Pittodrie outfit had also been linked with out-of-favour Rangers goalkeeper Cammy Bell.
"There was no approach for Cammy Bell, although I'm not saying his name wasn't mentioned," said McInnes.
New signing Collin began his career with Newcastle United and had loan spells with Oldham Athletic and Doncaster Rovers.
However, it was not until he joined Northern Premier League club Workington in 2004 that he made his senior debut.
McInnes would not comment on speculation linking Stuart Bannigan of Partick Thistle with a move to Aberdeen.
However, asked about the possibility of more signings during the January transfer window, McInnes admitted that injuries to Willo Flood and Ryan Jack had left his squad short in central midfield.
"We may be looking to bring one in and for nobody to go out," the manager added.
Meanwhile, McInnes also said any decision on the future of defender Paul Quinn will be made after Sunday's game with Ross County.
Quinn has been linked with a move back to the Dingwall club having joined the Dons from County in the summer.
Olympic silver medallist Samantha Murray has been selected in Great Britain's four-person modern pentathlon squad for this summer's Rio Olympics.
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Rotherham United goalkeeper Adam Collin has completed his switch to Aberdeen on loan until the end of the season.