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Hill, 18, won the skeet title at the inaugural European Games in June and claimed victory at the World Cup final in Cyprus last month.
She is joined by world medallist Elena Allen and world record holder Tim Kneale.
"Every competition I enter, I go in trying to win," Hill told BBC Sport.
"To be named as an Olympian is an incredible honour and I'm getting more confident I'm able to win these competitions."
The 2013 BBC Young Sports Personality of the Year added: "Hopefully I can inspire some other youngsters to get into a sport of some sort - it really does make you so determined and focused on what you want to do in life."
At London 2012, Peter Wilson came away with the team's only medal - winning gold in the men's double trap, before announcing his retirement in 2014.
Four of the six shooters will go to Rio having previous Olympic Games experience.
Steve Scott, a World Cup gold medallist in Cyprus in October, came 12th at the 2008 Beijing Olympics and will join debutant Kneale in the double trap competition.
London Olympian Allen competes against Hill in the women's skeet competition, while 2014 Scottish Commonwealth silver medallist Jen McIntosh will line-up in the 50m 3 positions event.
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Two-time Olympian and world silver medallist Ed Ling is Britain's competitor in the men's trap.
"I'm absolutely over the moon, it's a huge honour," said Ling.
"I know what I'm going to expect going into this year and to obtain that Olympic medal is what we work for."
Team GB are sixth on the all-time Olympic Games shooting medal table with 44 - 13 gold, 15 silver and 16 bronze.
The number of Rio Olympic shooters in the squad may increase next year, as results at the European Championships in Hungary in February could unlock two additional berths.
Shooting is the third sport to have British athletes officially selected for Rio 2016, after eight sailors and four canoe slalom athletes were named earlier in the year.
Amber Hill aims to become the first British woman to win Olympic shooting gold after being named in a six-strong Team GB squad for the Rio 2016 Games.