President Michael D Higgins said Annalise Murphy has "travelled the long and hard road to the Olympics" and has now "reaped the rewards of her many years of preparation and hard work".
Mr Higgins and Taoiseach Enda Kenny led the tributes to Ms Murphy after she captured the Olympic silver medal in the Women’s Laser Radial event on Tuesday.
Ms Murphy had produced a series of outstanding races and had overcome some of the world’s best competitors in the sailing class, President Higgins said.
"On behalf of the people of Ireland, I want to congratulate her on this achievement, and to thank her family and friends for their sustained support for her, and for helping her become such a positive role model for budding athletes everywhere."
Those comments were quickly followed by Mr Kenny who said winning Ireland's first sailing medal at the games since 1980 was a fantastic achievement and a testament to hard work, dedication and talent.
“Following on from her fourth place finish in 2012, I am delighted for Annalise, her family and for Irish sailing, that she has won a silver medal - just rewards for the considerable sacrifices made in pursuit of this Olympic success,” Mr Kenny said.
Minister for Sport Shane Ross and Minister of State for Sport Patrick O'Donovan also congratulated Ms Murphy.
“We all know how determined she was to bring home a medal, after coming so close four years ago this is a fantastic achievement for her,” Mr Ross said.
“Bouncing back from the disappointment [four years ago] to become European champion in 2013 [AND]now achieving a silver medal at the Olympics is a wonderful endorsement for what can be achieved through hard work and talent.”
Mr O’Donovan said to become the first Irish female to win an Olympic medal in sailing was “magnificent”.