The duo will link up with their parent club in the summer after spending the second half of the season out on loan.
Centre-back Brydon spent the first half of the season at Christie Gillies Park before a similar move to Edinburgh City, where he helped them win promotion to League One.
Midfielder Balde signed for Hibs in January from Strollers but remained on loan with the Lowland League outfit who finished joint-sixth in the division, level on points with former league side East Stirlingshire.
The Portuguese-born player spent time with Atlético Cacém and RD Algueirão before spells with Spartans, Rangers, Berwick Rangers, Bonnyrigg Rose, and Livingston before signing for long-term admirers Hibs earlier this year.
Strollers had some memorable results including a Scottish Cup win against SPFL opposition in Cowdenbeath, and were one of just three teams to beat title-winners Bonnyrigg during the season with a 3-2 victory in July.
Jardine said: “Thank you to our loan players and their clubs for supporting us once again.
"It was great to see Jack being promoted with Edinburgh City and hopefully he can hit the ground running when back in for pre-season.
"As a club we are extremely proud of Joao. While he’d be first to thank his team-mates, he’s earned and deserves his full-time contract and we wish him all the very best.”
Balde and Brydon are both likely to play for the reformed Hibs development team next term, and both players have been training with Hibs during their loan spells.