Forrester has impressed greatly this season, helping Tony McAndrew's under-18 side to the top of the FA Premier Academy League.
Academy Director Bryan Jones told Villa's website: "We are extremely pleased that Harry has signed his contract.
"Harry is a good passer, has great vision and can play in a variety of positions.
"But, as I say to all the academy graduates, there's still a lot to learn. He will have to work hard, put in lots of effort and perform well for Aston Villa.
"He's got a very good attitude and that should stand him in good stead."