World parallel bars champion Danell Leyva and John Orozco had already booked their tickets to the Games by finishing in the top two after the final day of men's competition at the US trials on Saturday.
Horton, Dalton and Mikulak then had to endure a nervous wait overnight until the USA Gymnastics selection committee announced their picks to round out the team.
It was especially nail-biting for Mikulak who took part in only one of the six events on Saturday, the pommel horse, due to a sprained left ankle and was therefore not eligible to qualify automatically.
"I'm just hoping that everything I have done in the past few weeks is enough for them (the selection committee) and they know that I am reliable and that it's just an ankle sprain," the 19-year-old said after the final day of competition.
"I will be back in no time and hopefully stronger than ever.
I will have plenty of time to be fully recovered if I am selected to go to London."
Mikulak, the 2012 US parallel bars silver medallist, hurt his left ankle on the vault, his last routine on the opening day of the trials, and his entire foot "puffed up like a balloon" by the following morning.
"I was like, 'goodness, this isn't good.' So I got in the training room and kept doing a bunch of rehab and they brought it down quite a bit," he said of efforts to get him ready for the final day of competition.
"In one day, they did so much but it just wasn't enough. We were trying to keep my health and the best interests of the team."
Horton, the 2008 Olympic silver medallist on the high bar, finished the US trials in third place with Dalton and Chris Brooks joint fourth.
Dalton was given the nod by the selectors because of his specialist strength on vault and floor exercise, and he headed the standings in both routines after the trials.
With Leyva and Orozco likely contenders for the all-round title in London and a squad bristling with strength in depth, the U.S. gymnasts have great expectations of winning a first Olympic team gold medal since 1984.
"It's certainly the best team since 1984," said Mitch Gaylord, a member of that triumphant US lineup in Los Angeles 28 years ago who now works for NBC as a television analyst.
Leyva has been humbled by such lavish praise.
"It's kind of unbelievable to hear that team say that about us," the 20-year-old said. "It's a huge honour and privilege that they think that way about us. We just have to make sure we live up to that."