The musician was sued by Daniel Ramos after the photographer said West attacked him outside an LA airport.
Gloria Allred, the lawyer representing Ramos, says the case has now been resolved a week before the trial was due to start.
She has released a photo of the pair shaking hands and smiling.
The lawsuit said that West attacked Ramos in 2013 after the paparazzo asked the rapper why he wouldn't talk to photographers.
"Celebrities are not above the law, and they have no right to physically attack someone simply because they were asked a question," Allred wrote in a statement.
Shawn Holley, West's lawyer, has not made a comment about the settlement.
In a statement, Allred says the other details relating to the legal agreement will not be made public, but the apology was an important part of the deal.
West, 37, pleaded no contest last year to misdemeanour battery over the attack. Misdemeanour generally means a less serious crime, while battery refers to any kind of unlawful physical contact.
He remains on probation.
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Kanye West has settled a lawsuit with a paparazzo with a handshake and an apology, the photographer's lawyer says.