The 24-year-old Australian started his career with Brisbane Broncos before joining Manly last season.
Parcell is likely to replace James Segeyaro who returned to his native Australia recently after the 26-year-old said he was homesick.
"I'm really excited about the style of football they want to play," Parcell told BBC Radio Leeds.
"I think what they're looking to do at Leeds will really suit me.
"Coming over to England has always been something that I've wanted to do but this has come about sooner than I expected."
He added: "I can understand after what's happened that fans might be worried I won't stick around, but I really think that this is going to suit me and I am excited about the prospect of living on the other side of the world.
"I don't think homesickness is going to be an issue."
Leeds Rhinos have signed Manly Sea Eagles hooker Matt Parcell on a three-year deal for an undisclosed fee.