Two-time Grand Slam champion Murray will look to retain his title as Olympic champion following his win over Roger Federer at London 2012.
Konta, who became the first British woman in 32 years to reach the semi-finals of a Grand Slam following her progression at the Australian Open, will compete in her first ever Olympic Games.
After being named in the squad, Andy Murray said: "Playing for Team GB during London 2012 gave me some of the best memories I have in sport.
"Being a home Olympic Games, it was such a special occasion and the atmosphere at Wimbledon was like nothing I have ever experienced.
"I watched Mo [Farah], Greg [Rutherford] and Jess [Ennis-Hill] win gold the night before my final and it definitely helped inspire me. Winning medals for your country is as good as it gets and I can't wait to get to Rio to try and win more medals."
Murray also won silver with Laura Robson in the mixed doubles four years ago.