A $10 million check from the archdiocese was given to the plaintiffs' attorney, Mitchell Garabedian.
Sweeney addressed the alleged victims who appeared in court, saying she wanted to acknowledge their pain and make clear that the settlement means the court recognizes that Geoghan did what they say he did.
"I hope you are able to recognize in yourselves not just the hurt that was done to you but your own resilience, your courage," she said.
An earlier settlement worth up to $30 million had been announced in May, but the archdiocese backed out of that deal soon afterward, saying it could not afford the deal because of hundreds of other lawsuits being filed.
Garabedian said the plaintiffs agreed to the lower figure because they want to try to put the abuse behind them.
"They want closure, and they understand that the church does not really care about their emotional well-being," Garabedian said.
The archdiocese issued a statement saying Cardinal Bernard Law is grateful a settlement could be reached.
"His Eminence continues to pray for survivors of sexual abuse and he hopes that for those who have suffered the affects of such sinful and evil acts, that today's settlement will be a significant moment in their healing process," the statement said.
Several alleged victims said they were not comforted by Law's words or the settlement.
Mark Keane said the settlement will not even pay for the therapy that the victims will need for the rest of their lives.
"I feel I need to apologize to all future victims of church sexual abuse for setting such a low settlement amount," he said. He said the victims agreed to the lower settlement because they are "tired and emotionally spent."
Nancy Greenlaw, the mother of John Brian Greenlaw, confronted archdiocese attorney Wilson Rogers Jr. with a picture of her son as Rogers left the courtroom. Her son died of a drug overdose that she blames on abuse by Geoghan.
"This is my son," she told Rogers. "He passed away last year. I want everybody to remember his face. I want everyone to know the church and its actions killed my Brian."
Rogers responded, "I'm sorry. I'm terribly sorry."
The bulk of the settlement - $9.3 million - will be divided among 50 people who say they were molested by Geoghan. Twenty people who say Geoghan exposed himself to them will split $540,000, and 16 parents of children who say they were abused by Geoghan will divide $160,000.
After the archdiocese withdrew from the original deal in May, Garabedian asked Sweeney to enforce the settlement. Sweeney held a five-day hearing on the request last month and was expected to issue her ruling soon. But the two sides worked out a new agreement in the meantime.
Geoghan was convicted in January of groping a 10-year-old boy in a swimming pool in the early 1990s. The now-defrocked priest was sentenced to nine to 10 years in prison.
The sex scandal engulfing the nation's Roman Catholic Church erupted when it was learned that church officials had moved Geoghan from parish to parish despite knowing of abuse allegations against him.