Midfielder Gardner has risen through the ranks at Villa Park and made 18 appearances for the first-team so far.
The 22-year-old has seen his progress hindered by a series of knee injuries and was sent on loan to Championship outfit Sheffield Wednesday last season.
Having regained fitness, the former England Under-21 international is targeting a regular spot in Paul Lambert's starting XI.
"I'm buzzing. The club have been brilliant with me," he told Villa's official website. "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.
"Obviously injuries have hampered my progress but I've learned a lot from my experiences and I'm definitely stronger. The club have been superb so now I want to kick on."
Forward Robinson is also a product of Villa's youth team, and made his senior breakthrough last term.
"I am absolutely delighted to sign a new deal here," the 19-year-old commented. "Now it's about pushing on and progressing.
"Last season was fantastic. I didn't expect so many positives to come out of it. To work as hard as I have and then have the gaffer give me a chance with the first team, it was amazing. I have loved every minute of it."
