Multiple people throughout history, including Leonardo da Vinci, have designed parachutes. The modern parachute was not patented until 1920. This version included a ripcord, a folding parachute, and a harness. According to Google Patents, this was filed under patent number US1340423A. The inventor is listed as Floyd Smith. The patent has since expired, and this is a common framework for parachutes in use today.

Sources: 
Leonardo Da Vinci's Life. (n.d.). Retrieved from http://www.davincilife.com/davincis-parachute.html
US1340423A - Parachute. (n.d.). Retrieved from https://patents.google.com/patent/US1340423A/en

Image Source:
US1340423A - Parachute. (n.d.). Retrieved from https://patents.google.com/patent/US1340423A/en