The settlements must be approved by a City Council vote Thursday, the Chicago Tribune reported.
Christina Eilman, who was kidnapped and raped in a housing project and then fell seven stories, is to receive $22.7 million, officials said.
Eilman, who suffers from bipolar disorder, had been arrested at Midway Airport seven years ago when she was 21 after acting strangely and being prevented from boarding a flight home to California. Her parents had called police and told them she was bipolar.
Eilman's lawyers say she is permanently physically disabled and the attack also worsened her psychiatric problems.
A federal judge who dismissed the city's argument that police were not responsible for the attack by a gang member said officers "might as well have released her into the lion's den at the Brookfield Zoo." Two City Council members said Tuesday the judge's language was "racially insensitive."
Corporation Counsel Steve Patton said settlement talks last week with Eilman's parents were "the most emotional" he has seen. He said police now have crisis teams to help officers deal with the mentally ill.
"We did right by the city and her taxpayers, and we did right by this young woman and her family, and ended up with a settlement that will provide for her for the rest of her life," Patton said.
In the other case, Alton Logan will receive $8.25 million. Logan, who has been declared innocent, was convicted of murder and spent 26 years in prison.
Logan's lawyers say police had evidence another man had committed the crime at the time their client was arrested. The case was one of many involving former Police Commander Jon Burge, who is now serving a federal prison term.
Chicago has paid $60 million in damages and legal fees to people who say they were physically tortured by Burge or mistreated in other ways. Four cases are still pending.
"The reprehensible conduct of Mr. Burge and the detectives under his command 25 or more years represents a dark chapter in the history of our great city," Patton said. "Their actions served to undermine the level of trust between the city and the police department and our citizens, particularly our citizens in African American neighborhoods."
Duggar sisters unveil Christian dating rules in new book
Attkisson leaves CBS News, reportedly over network's 'liberal bias'