"I don't think it's really sunk in yet, but I have a huge sense of relief."
The Victorian said her husband and coach, 2000 Sydney Olympian Simon Gerada, was a huge inspiration in qualifying for the able-bodied games.
"To be honest the only person who thought I could do it was Simon," she said.
"Even coming into this week I didn't give myself a chance. Now I'm just stoked that I get to go to the Olympics."
Tapper will join 12 others to have competed at both the Paralympics and Olympics, including New Zealander Neroli Fairhall who became the first paraplegic to participate at an Olympic Games in 1984.
Fairhall won a Commonwealth Games gold medal in archery, while Hungarian fencer Pal Szekeres became the first person to have won medals in both the Olympics and Paralympics.
In recent times, South Africans Natalie du Toit (Swimming) and Oscar Pistorius (Sprinting) have been high-profile Paralympic athletes to participate at the Olympics.