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Barnes has the chance to make Irish Olympic history in Brazil by becoming the first athlete from his country to win medals at three successive Games.
The 29-year-old won light-flyweight bronze medals at both the Beijing and London Games.
His fellow boxer Katie Taylor carried the Irish flag at the opening ceremony in London.
Barnes' achievements include winning the European Amateur Championships in 2010 in addition to clinching gold at both the 2010 and 2014 Commonwealth Games.
A hugely popular figure in Irish sport, Barnes received an MBE in Queen Elizabeth's New Year's Honours list in December 2014.
Olympic Council of Ireland president Pat Hickey suggested in 2012 that golfer Rory McIlroy should be a candidate to carry the Irish flag in Rio.
However, Hickey said on Wednesday that he was "delighted to announce" that Barnes had been selected for the role.
"His commitment to the cause of Irish boxing and Irish sport makes him a role model for aspiring young athletes in Ireland and the natural choice as Ireland's flag bearer," said the OCI president at an event in Dublin marking 100 days from the start of the Rio Games.
Barnes described the news as an "incredible honour".
"It's an amazing feeling to represent Ireland at an Olympic Games and I've been lucky enough to experience it twice before already," added the Belfast man.
"I will be going for gold in Rio in the ring but I will also have the responsibility of helping to build a really positive environment for all Irish athletes. I could not be more excited about the next 100 days."
Belfast boxer Paddy Barnes will be Ireland's flag bearer at this year's Olympic Games in Rio.