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."
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