Midfielder Grimes has been captaining the club's Under-18s this season while goalkeeper Pym was called into the first-team squad to deputise in February when Artur Krysiak missed a match through injury.
The players in the second year of the club's Academy were given the news of their deals on Thursday, with right-back Sam Brown also handed a short-term deal.
Centre-backs Irvine Densu and Kamarl Duncan were not given professional contracts.
"Everyone at Exeter City Football Club would like to extend their utmost gratitude to all five players for their hard work and dedication during their time with the Academy," a club statement said.
"The club will continue to support Irvine and Kamarl beyond their time with Exeter City, and wish them the very best for their future careers in football."
- Sports & Recreation
- Artur Krysiak