Cox had already been selected in the ParalympicsGB athletics line-up as a sprinter and the 25-year-old from Chapeltown has now had her place in the cycling team confirmed.
Louis Rolfe was also named as the British Paralympic Association (BPA) revealed their two final riders for the cycling team
“I’m delighted to be selected and be on the plane to Rio,” said Cox, who ParalympicsGB believe will be the first British athlete to compete in two sports at a Games since 1992.
“I’ve already won a world title in cycling earlier this year and I’ll be giving everything I’ve got to add a Paralympic gold medal to my collection,” continued Cox, who was diagnosed with multiple sclerosis at the age of 23.
Rolfe completes the team sprint line-up alongside Jody Cundy and Jon-Allan Butterworth, and will also compete in the individual pursuit on the track and time-trial on the road.
Cox and Rolfe are the final two additions to the cycling team, the majority of which was announced in mid-June.
Britain’s most-decorated female Paralympian, Dame Sarah Storey, will be gunning to add to her tally of 11 gold medals.
Rio is a long way to go for 21 seconds and one length of the pool, but Ben Proud hopes the 5,500-mile journey from Devon is worth it.
The 21-year-old Plymouth Leander swimmer will race in the 50m freestyle at his first Olympics. Proud said: “It’s what I train for, it’s what I fly for. All my training for the past four, five years has been around that one 21-second race. Hopefully it goes well.”
The Malaysia-born swimmer takes confidence from his results at the 2014 Commonwealth Games in Glasgow, where he won golds in the 50m freestyle and 50m butterfly (a non-Olympic event).
He was eighth in both one-length events at the 2015 World Championships and third behind 2012 Olympic gold medallist Florent Manaudou of France at May’s European Championships in London.
“Every meet I’ve been to has just added that little bit of confidence, building up to Rio,” Proud added.
“Everything gearing up to this Olympics has gone to plan and hopefully everything will click in the summer.”
Meanwhile, The World Anti-Doping Agency have cancelled their scheduled Rio 2016 pre-Games press conference on Thursday to avoid it being overshadowed by the ongoing Russian doping crisis.
WADA came in for criticism from International Olympic Committee president Thomas Bach on Sunday for failing to act more quickly on evidence of widespread doping in Russia provided by whistleblower Yuliya Stepanova.
Bach said the IOC was not responsible for the timing of the WADA-commissioned McLaren report and could, therefore, not be held responsible for the scramble to assess the eligibility of Russian athletes to compete in Rio 2016 just days before the Games are due to start.
The International Association of Athletics Federations imposed their own ban on the Russian track and field team and more than 100 Russian athletes across all sports have so far been excluded from the Games.
The IOC asked international federations to make their own rulings on Russian athlete eligibility for Rio 2016.