The 16-year-old is the current senior British floor champion and won bronze at the 2015 World Championships.
She missed the European Championships in June to concentrate on school exams.
"I had the opportunity to watch the all-around final in 2012 and it was incredible," she told BBC Sport.
"From that, it made me want it even more, it was incredible and made me so motivated."
Tinkler is one of five women in the gymnastics team, along with sisters Becky and Ellie Downie, Commonwealth champion Claudia Fragapane and Ruby Harrold.
She continues to train with South Durham coaches Nicola Preston and Rachael Wright in her native north east.
"Me and my coaches have taken each day as it comes and we've not really spoken about Rio," Tinkler added.
"Getting to the World Championships was incredible and we didn't think that was going to happen so it's amazing."
Bishop Auckland gymnast Amy Tinkler was inspired by watching the London 2012 Olympics and is excited for taking part herself following her selection for the Team GB squad at Rio 2016.