The settlements will go to the full city council on Wednesday for final action.
One point eight million dollars will go to a man whose double murder charges were dropped three years ago.
The larger of the two settlements goes to Michael Tillman. He spent more than 23 years in jail based on a tortured confession.
In January of 2010, Tillman walked out of prison a free man, cleared of the rape and murder charges that sent him to jail in 1986. Tillman confessed to charges after being tortured for days by Burge.
"They put a bag over his head to suffocate him. They beat him bloody with a telephone book. They took him outside the police station by some railroad tracks, put a gun to his head and threatened to kill him," said Flint Taylor, Tillman's attorney.
Tillman was exonerated after spending 23 years in prison. He filed lawsuits against Burge and former Mayor Richard Daley.
On Monday, the City Council finance committee approved a settlement of more than $5 million. But that settlement means Daley will avoid having to give sworn testimony, answering questions from attorneys of other alleged torture victims.
In a statement, Tillman said: "If he had done what he should have, I would not have been tortured, lived with the fear of the death penalty, or sent to prison. To me, this settlement proves that Daley, Jon Burge, and Burge's torture crew did me terribly wrong."
"We're disappointed that we're not going to be able to question Mayor Daley, but we know that he remains a central figure in the torture scandal," said Taylor.
Members of the finance committee say the settlement is a way to move beyond a dark chapter in the history of the police department.
"This has been an eyesore on the city of Chicago for a really, really long time, and it's time for us to move forward and get some closure," said Ald. Leslie Hairston, 34th Ward.
"That's the whole purpose of settling this case. Not to say a person didn't need to be deposed, but it's about healing our city and moving forward," said Ald. Anthony Beale, 9th Ward.
In response to the settlement, Daley's spokesperson Jacquelyn Heard said: "The former mayor has cooperated in all aspects of this case. He was prepared to give his deposition. As for the claims that he knowingly allowed police torture to occur some 30 years ago, his response remains the same: It is simply not true."
Burge was convicted in 2010 of lying about the torture of suspects and is serving a four-and-a-half year sentence in prison. However, he continues to draw his $3,000 a month pension.
Five torture cases remain unsettled and it's possible Daley could still be deposed in other cases.