Testimony in the civil trial on behalf of Christopher Harris began last week, and the settlement was reached Tuesday morning.
King County spokeswoman Christine Lange said the county agreed to pay $10 million to settle the case. The Harris family had been seeking $25 million.
"We believe that this outcome is the best possible resolution to this case," Lange said.
Harris suffered permanent brain and spinal damage in the May 2009 incident, and can no longer talk, walk or feed himself. Harris' doctors say he will need 24-hour care for the rest of his life.
"The $10 million that they've agreed to pay will be used for Chris' medical expenses, which will be extensive, because he is expected to live a very long time," said Harris' attorney Sim Osborn. "What we did today allows (the Harris') to live an independent life and lets Sarah take care of her husband at her home with (their) families nearby."
Osbron said there are no winners in the case.
"Christopher Harris is still in a bed, he is still paralyzed, he still can't talk, he still can't feed himself," he said.
Harris was injured when he was hit by King County Sheriff's Deputy Matthew Paul. Surveillance video from the Cinerama movie theater in Downtown Seattle showed Harris racing toward Paul, who appeared to have stopped with his arms outspread, and of giving him a shove that knocked the smaller man eight feet and through the air into the base of a wall.
County prosecutors declined to file charges against Paul, saying there was no legal basis for a criminal charge.
Susan Harris said Tuesday's settlement should prompt another investigation.
"I feel like for the sheriff's department to agree to pay this money, it should say that an investigation should be done into what happened," she said. "I don't know how they would agree to pay that amount and not feel like something was wrong."
Witnesses said the incident began when several men, some covered in blood, ran into a convenience store where Harris had been shopping. Deputies chasing down the suspect were mistakenly told by witnesses that Harris was the man they wanted. Harris had not been in the fight, but he ran.
The surveillance video shows the end of the chase as moviegoers are exiting from the Cinerama theater, about 2½ blocks from where the chase began.
Harris comes into view, makes a slight turn and slows down as Paul gives him a fierce shove, knocking him off his feet. Harris' head slams into the base of a tiled wall outside the movie house.
Two witnesses say Harris seemed to be stopping and said, "I don't have anything, I didn't steal anything," just before he was hit by Paul, who weighed about 270 pounds, about 100 pounds more than Harris.
One deputy acknowledged on the witness stand that the deputies did not identify themselves to Harris before they started chasing him.
Lange said the settlement still needs to be approved by the court and would be paid from by the county's self-insured fund and an outside insurance provider.
In a written statement, King County Sheriff Sue Rahr apologized to the family.
"We realize that the incident where Christopher Harris was injured by one of our deputies was a tragedy for Mr. Harris, his wife Sarah, and his entire family. We hope the settlement will at least bring financial peace, while understanding nothing we can do or say can make that night 'go away,'" she said. "My sincerest condolences and apologies to Chris and his family."
George Collett, a juror who was hearing the case, said he's glad the two sides were able to reach a settlement.
"I don't think that the officer intentionally tired to hurt the guy," he said. "I think his adrenaline was going, and he just used too much force."
Susan Harris said she'll have to live with the consequences.
"They took away the greatest person I've ever met in my whole life, and our future together."