Rhinos have paid an undisclosed fee for the 21-year-old, who is the son of Eagles coach Mark Aston.
The Sheffield-born scrum-half has scored 31 tries in 69 games for the Eagles in the Championship since making his debut in 2013 as an 18-year-old.
He is also a talented goal kicker and landed 93 two-pointers for the Eagles last season.
Aston – who began his career with the Hillsborough Hawks community club – said: “This is a great opportunity for me.
“It is a dream come true to sign for Leeds Rhinos and to get the chance to play in the top-flight having played in the Championship for the last few years.
“I have had a good chat with [Rhinos coach] Brian McDermott and I am looking forward to learning from him.
“I have been at Sheffield all my life and obviously only had one coach in my dad so it will be a fresh start with a different voice and new concepts and systems about how to play the game.
“I am excited about the challenge of playing in Super League and testing myself in training and in games against the best players around.”
Eagles were full-time in 2016, when they reached the Championship Shield final, but Aston admitted it will be a big step up from the second tier.
He added: “The Championship is a different competition and I have heard people say that it is more physical, but not as fast as Super League.
“I am looking forward to discovering that for myself now. I think the fact I have played nearly 70 games in the Championship, but I’m still only 21 will stand me in good stead for the future.”
McDermott regards Aston as a rising star.
“Considering his age, Cory has already got a lot of experience of playing senior rugby which is testament to his toughness, especially as a half-back in the Championship,” he said.
“It will be good to see him in our full-time training environment and he is looking forward to the challenge of coming away from home in Sheffield for the first time and making the most of his chance in Super League.
“As with all our young players, we will certainly help him to make the most of his potential and the rest will be down to his hard work and determination to succeed.”
Mark Aston said: “I am delighted for Cory that he has this opportunity to play in Super League with one of the biggest clubs in the country.
“It shows that perseverance and hard work can help you realise your ambitions.
“He has taken a different pathway by playing in the Championship at a young age, but that will stand him in good stead and hopefully lead to a long and successful career at Leeds Rhinos.”
Aston is Rhinos’ second signing for 2017, following forward Jack Ormondroyd from Eagles’ Championship rivals Featherstone Rovers.