The deal is for the remainder of the current season, with a view to a long-term extension for both players.
Hardaker, 24, has scored 67 tries in 155 games for Leeds and was named Man of Steel in 2015, but he requested a move to the NRL earlier in June.
Segeyaro, 25, has played in only four league games this season.
The Papua New Guinea-born player won the Dally M Hooker of the Year award in 2014, having scored 10 tries in 25 games.
"Zak goes with out best wishes and I am pleased for him that he has been able to fulfil his ambition of playing in the NRL," Leeds head coach Brian McDermott said.
"When Zak came to us to request a move, it was always going to be important that we were able to strengthen our group.
"In James Segeyaro, we have a great opportunity to bring in a highly-rated player."
Leeds and England full-back Zak Hardaker has joined NRL side Penrith Panthers with immediate effect in a swap deal for hooker James Segeyaro.