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.
Olympic silver medallist Samantha Murray has been selected in Great Britain's four-person modern pentathlon squad for this summer's Rio Olympics.