United said earlier on Thursday that it would offer passengers who give up their seats up to $10,000, reduce overbooking of flights and no longer call on law enforcement officers to deny ticketed passengers their seats.
Southwest Airlines also said on Thursday that it would end overbooking of flights.
Dao, a 69-year-old Vietnamese-American doctor, was injured when Chicago aviation police removed him from his seat and then dragged him from the plane to make space for four crew members on the flight from O'Hare International Airport to Louisville, Kentucky.
United has taken "full responsibility for what happened on Flight 3411, without attempting to blame others, including the City of Chicago," Thomas Demetrio, an attorney for Dao, said in a statement.
Demetrio said there was no need to proceed with separate litigation against the city. Republic Airways, United's regional partner, which operated the flight that Dao was on, has also been released from responsibility as part of the settlement, Demetrio's office said.
Chicago officials did not have an immediate comment.
United said in a separate statement that it was pleased to reach "an amicable resolution of the unfortunate incident that occurred aboard flight 3411."
Munoz stressed that point in a letter sent on Thursday to customers, saying the airline would increase its focus on their satisfaction.
"We can never say we are sorry enough for what occurred, but we also know meaningful actions will speak louder than words," he said.
Separately, officials at 10 of the busiest US airports said their rules prevent security officers from physically removing passengers from airplanes unless a crime is committed.
(Reporting by Timothy Mclaughlin in Chicago; Additional reporting by David Shepardson in Washington; Editing by Richard Chang)
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