The Republic of Ireland international was a free agent after his contract expired with Villa.
Speaking to HeartsTV, Whelan said: "I'm delighted. I just want to get my head down and now and stuck into things. I've managed to train for the last couple of days with the lads so I've got the meet and greet out of the way so I'm delighted to get everything sorted now.
"Once I knew Hearts were involved then It was something that I really had to think about. The manager's been great, he's given me a lot of time to think about things but for the last week or so I've been ready to go.
"The manager has been crucial to getting me up here, to be honest. He's shown a lot of ambition in where he wants the club to go. I came up and trained with the lads for a couple of days last week and I was really impressed. I'm up here now and I'm ready to go to dig in and get some results."