Body camera video of the traffic stop showed Samuel DuBose, 43, was shot in the head by officer Ray Tensing in July last year after he was pulled over for a missing front licence plate on his car.
Mr DuBose attempted to prevent the officer from opening the car door before the car started slowly rolling forward. Mr Tensing, who is white, pulled his gun and fired once.
Mr DuBose’s death fuelled demonstrations and intensified a debate on policing and race in the US that helped lead to the founding of the Black Lives Matter movement.
Lawyers for the family said in a statement that the settlement, including the free tuition, is worth about $5.3m.
The agreement must be approved by the Hamilton County Probate Court before it is finalised.
The agreement includes an apology to the family from the school president Santa Ono.
The university will work with the family to establish a memorial on campus commemorating Mr DuBose, the statement said.
“This agreement is also part of the healing process not only for the family but also for our university and Cincinnati communities,” Mr Ono said in a statement.
The case was mediated in closed-door sessions over a two-day period, family lawyer Billy Martin said.
Mr Tensing has pleaded not guilty to murder and voluntary manslaughter charges and is free on a $1m bond. No trial date has been set. If convicted, Mr Tensing faces a possible life sentence.
An independent report on the shooting released in September called it “entirely preventable”.