Gardner put the finishing touches to his contract, which was agreed in May, while Robinson returned from a summer break to put pen to paper.
Gardner, 22, has been at Villa since he was seven-years-old and has made 18 appearances for the first team, while Robinson, 19, has been at Villa since he was eight-years-old and made his senior breakthrough last season, appearing five times.
Gardner told Villa's website: "I'm buzzing. The club have been brilliant with me.
"I've had a bit of bad luck in the past two years but I'm feeling good and strong now so hopefully I can repay them."
Robinson also said: "I am absolutely delighted to sign a new deal here.
"Now it's about pushing on and progressing."
For the big stories and the banter follow us on Twitter: @tribalfootball
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!