Midfielder Gardner, 22, committed to a new contract having agreed to extend his stay at Villa Park in May, while 19-year-old forward Robinson has done likewise since returning from holiday.
Both players have come through the club's underage system, with Gardner making 18 appearances for the Villa first team since making his debut in 2011 and Robinson five senior appearances following his debut against Tottenham in the Capital One Cup in September 2013.
Gardner, who is the brother of former Villa and Sunderland midfielder Craig, told the club's official 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.
"I've been here from a young age and I've been to Villa games all my life as a fan so it is a dream come true to play for the first team like I have done."
Robinson said: "I am absolutely delighted to sign a new deal here. 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."
Paul Lambert's side start their 2014/15 campaign away at Stoke City on August 16.