The church had been accused of trying to cover up the allegations against the priest, 52-year-old Rudolph "Rudy" Kos, who is now serving a life sentence in prison. Earlier this week, the Vatican stripped him of his priesthood.
It is one of the largest settlements ever paid by the church in a sexual abuse case.
"For the moment, it brings an end to the very active phase of what took place _ the trial, the aftermath and the settlement," Bishop Charles V. Grahmann said. "But a lot of healing has to take place, a lot of reconciliation."
The bishop also apologized for Kos' behavior and for the way the diocese handled the allegations.
Eight of the former altar boys were among 11 victims who won $119.6 million in a lawsuit a year ago in the biggest verdict ever against a diocese. A ninth former altar boy also shared in Friday's settlement.
The eight settled for less than the full judgment for fear the diocese would file for bankruptcy before paying out any money, their lawyers said. The diocese previously settled with the three other plaintiffs for a total of $7.5 million.
Nineteen-year-old Nathan Nichols, one of the alleged victims, said he was happier than he has been in more than six years.
"I believe it's a day of relief for everybody," he said. "Finding out that the bishop has apologized for the wrongdoing helps us get on with our lives."
He added: "The pain will never go away. The dollar amount can't help that. The only thing that can is seeing that the diocese is changing."
In 1996, the Archdiocese of New Mexico reported it was nearly bankrupt and was forced to sell some propertly after settling more than more than 150 molestation claims. The settlement amounts were not disclosed, but counseling costs and legal fees alone ran into the millions.
As part of the settlement in Dallas, the diocese agreed to take steps to reduce the risk of sex abuse in the church, including the establishment of review boards to handle assignment of clergy and complaints, and background checks of employees and volunteers.
Complaints about Kos' behavior first surfaced in 1992. Four victims told police they were molested about 1,350 times over five years. The parents of the victims claimed the church ignored the allegations and tried to sweep them under the rug.
Kos had denied the allegations but was convicted of aggravated sexual assault last year during a criminal trial and sentenced to prison.
After the civil verdict, the diocese said it could not pay the judgment, claiming it had only about $6 million in total assets.
Under the settlement, the diocese will pay $7.25 million, and insurance companies will pay the rest, the bishop said.
"This settlement brings closure to a long period of sadness for all of us. There are no simple solutions when confronting terrible acts such as those inflicted by Rudy Kos," Grahmann said.