Spaniard Garcia-Thompson and 30-year-old Grotowski, who lives in Florida, are the first men to compete for Britain in the event in Olympic Games history.
Previously Garcia-Thompson, 33, has competed for the country of his birth, and he currently resides in Tenerife, but he took 18 months out of the game so he could join forces with London-born Grotowski to fight for Team GB selection.
They were the 540th and 541st out of 542 athletes selected for the home nation, and both feel ready to prove their worth.
"The Spanish federation was agreed and the British one had no problem," said Garcia-Thompson, who lived in Nottingham as a youngster.
"You have to stop competing for 18 months and after that you can play, and that is what I did.
"Some people have been asking how British we are, but we are very proud and feel 100 per cent."
Grotowski added: "I moved from London to Yorkshire when I was about seven, lived there for about two years then moved to the States when I was nine.
"We both feel absolutely British."