The 20-year-olds arrived at the end of September on initial one-month deals.
Both players have featured in every League Two game since then, with forward Jervis scoring three goals in all competitions.
Meanwhile, midfielder Ibrahim Atiku has been released by the club three months into his two-year deal.
The Ghanaian failed to make an appearance during his time at the County Ground.
Commenting on the deals for Ridehalgh and Jervis, manager Paolo di Canio told BBC Wiltshire.: "They are happy to stay here and we are happy to keep them.
"Jake came into my dressing room after training and said 'boss, I want to stay' and I said 'yes I understand, but it is three times now you have come in in 10 days'.
"Obviously Birmingham City are happy to leave Jake here because he has regular football and has improved a lot.
"Liam is the same - he wanted to stay so that is very positive because they have found a fantastic group and they felt part of this plan straight away."