Keatings, who is named as a reserve, won all-around world silver in 2009 and became European pommel horse champion one year later in Birmingham.
But he has suffered with a succession of injuries since and despite an encouraging performance at the recent British Championships, when he placed third, he was not among the five British gymnasts named.
"I achieved loads of the selection targets, more than most of the team but it wasn't enough to impress the selectors," he wrote on Twitter.
"I wish the team all the best and I'll be supporting them all the way and I hope they achieve some great things.
"I'm going to try and smash up the next four years and hopefully have more luck with no injuries and do a job in Rio."
Three-time national all-around champion Daniel Purvis and pommel specialist Louis Smith, who won bronze in Beijing, will lead the British men's team.
They will be joined by Youth Olympic champion Sam Oldham, Kristian Thomas and three-time Commonwealth Games medallist Max Whitlock, meaning there is also no place for Ruslan Panyeyleymonov.
"It’s been such an intense time in the lead up to the announcement with such a strong squad to pick from," said Smith.
"Now we’ve got to do the business at the Games, which we’re all capable of.
“It’s just been a crazy four years since Beijing, for me and especially for gymnastics in this country.
"I’m not sure anyone ever expected such rapid development and it’s such a positive thing for everyone involved in the sport. Now we have a chance to really show how far we’ve come."
Three-time world champion Beth Tweddle will front a women's team that includes double Commonwealth champion Imogen Cairns, Hannah Whelan, Jennifer Pinches and Rebecca Tunney.
Tunney, who recently won the national all-around title, becomes the youngest member of Team GB named so far aged just 15.
"After 2008 I wasn’t even sure I would carry on, but the huge support for London and the enthusiasm of the public has really motivated me and inspired me to carry on training hard," said Tweddle, who is competing at her third Games.
Former world number one Katherine Driscoll will be Britain's sole representative in trampolining while Frankie Jones takes the individual host nation quota spot in rhythmic gymnastics.
Having won their legal appeal to compete at the Games, Georgina Cassar, Jade Faulkner, Francesca Fox, Lynne Hutchison, Louisa Pouli and Rachel Smith will form the first ever British team in the rhythmic gymnastic group competition.
“We are extremely proud to be able to name such a strong team to compete for Team GB in the gymnastics disciplines in London," said British Gymnastics performance director Tim Jones.
"The competition for places has been intense and we had both the luxury and challenge of so many great gymnasts to select from.
“This Olympic cycle to date has been the most productive and successful ever for British Gymnastics at international level, and we go into the Games in great shape with more gymnasts capable of making their mark than ever before.
"The mood in the camp is positive and we are all looking forwards to building our reputation ever further with a strong showing at London 2012.”