Murray, who won a memorable gold at London 2012 after beating Roger Federer in the final, will play singles, doubles with Jamie and likely partner world number 18 Johanna Konta in the mixed doubles in which he was silver medallist in London.
Heather Watson has also been selected.
Murray, beaten in the French Open final last weekend by Novak Djokovic, led Britain to the Davis Cup title in November and has targeted the Olympics as one of his goals this year.
"There is invaluable Olympic experience in this squad with both Andy and Jamie selected for their third, and Heather for her second successive Olympic Games," Mark England, Chef de Mission for the British Olympic team, said in a statement.
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"Double medallist Andy is the defending men's singles champion and Jamie one of the world's best doubles players.
"Heather I am sure will lean on the experience from London 2012 and use that to her advantage; and it is brilliant to welcome Johanna into the team for the first time after a sensational year so far."
Murray, who claimed his first grand slam title at the U.S. Open shortly after winning gold in London, is ranked two in the ATP rankings, the same as brother Jamie in doubles.
"Playing for Britain during London 2012 gave me some of the best memories I have in sport," Murray, 29, said.
"I can't wait to get to Rio to try and win more medals."
(Reporting by Martyn Herman; Editing by Toby Davis)
