The suit, to be filed Monday, will name the city, the New York Police Department, current and former police officers and the Manhattan district attorney's office, attorney Jonathan Moore said.
The three men - Kevin Richardson, Raymond Santana and Antron McCray - were among five convicted in the near-fatal attack on the 28-year-old jogger. The attack - allegedly by black and Hispanic youths against a white woman - stirred fears of racial violence in the city.
The five men were cleared by a state judge last year after another man, Matias Reyes, who was already jailed for other crimes, confessed to the Central Park attack. DNA evidence supported his claim.
All five served prison time. Richardson, Santana and McCray served about seven years each, Moore said.
"We want to compensate them and their family members for having to live through many, many years of incarceration and many years of being labeled sexual predators when it was never true," Moore said.
Moore said the lawsuit would accuse the defendants of "malicious prosecution" and "conspiracy to cover up the truth." He planned to announce more details at a Monday news conference.
A spokeswoman for New York City law officials, Kate O'Brien Ahlers, said the city had not seen the legal papers and would evaluate them once they are filed.
The two other cleared youths, Yusef Salaam and Kharey Wise, are expected to file similar lawsuits later but are being represented by different lawyers, Moore said.
By Erin McClam