The 21-year-old scored 31 tries in 69 games for the Eagles, who are coached by his father Mark.
"This is a great opportunity for me," Aston told the club website.
"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."
Leeds Rhinos have signed Sheffield Eagles half-back Cory Aston for an undisclosed fee on a two-year deal.