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."

House of Representatives Speaker Paul Ryan said the executive orders, which bypass Congress, "undermined liberty" and would be challenged in court.
Republican presidential frontrunner Donald Trump said that, if elected, he would reverse the measures.
In an emotional address on Tuesday, Mr Obama accused the gun lobby of holding the country hostage.
Wiping away tears, he recalled the 2012 Sandy Hook primary school shooting in which 20 children and six adults were killed.
President Obama's executive actions involve:
He previously told the BBC that the failure to tackle gun control had been the greatest frustration of his presidency.
Why Obama is powerless - the roadblock at Congress
Are you mad or criminal? - the question a gun seller asks
Texas women and their firearms - a photographer taught to shoot at an early age
Do tighter gun laws work? - a state where guns are a way of life
Guns at home - the question parents hate to ask before a playdate
However, the largest gun lobby group, the National Rifle Association (NRA), said Mr Obama's steps would not have prevented any recent mass killings in the US.
"Rather than focus on criminals and terrorists, he goes after the most law-abiding of citizens," said Mr Ryan, a Republican.
"His words and actions amount to a form of intimidation that undermines liberty."
Correspondents say the announcement is already shaping up to be an issue in the 2016 presidential election.
Donald Trump said that he would "un-sign" the measures if elected to the White House - a sentiment echoed by other Republican presidential candidates.
Senator Ted Cruz tweeted that the executive actions were unconstitutional, with a link to sign up for his campaign correspondence on a web page that says "Obama wants your guns".
Former Florida governor Jeb Bush, also a Republican candidate, tweeted that he would repeal the actions and protect the Second Amendment.
Leading Democratic candidate Hillary Clinton tweeted: "@POTUS is right: We can protect the second Amendment while protecting our families and communities from gun violence. And we have to."
President Obama announced the law change at the White House, surrounded by survivors and relatives of victims of shootings.
"The gun lobby may be holding Congress hostage right now, but they can't hold America hostage," he said.
Gun violence is significantly higher in the US than in other advanced countries, killing about 30,000 people each year.
Sales of guns in the US appear to have risen recently amid speculation that the White House was going to tighten the law.
Shares in gunmaker Smith & Wesson rose to their highest value since 1999 ahead of President Obama's announcement.
Congress has been reluctant to pass any laws restricting gun ownership, facing pressure from gun owners and the NRA.
Leeds and England full-back Zak Hardaker has joined NRL side Penrith Panthers with immediate effect in a swap deal for hooker James Segeyaro.
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Leading US Republicans have denounced President Barack Obama's move to tighten gun controls.