"My clients feel as though it's time for closure. They want to remove themselves from this darkness and try to heal," Mitchell Garabedian told Reuters news agency.
The judge handling the sex abuse allegations concerning John Geoghan - currently serving a six-year prison sentence for molesting a 10-year-old boy - is due to conduct a hearing on Thursday.
An offer of $30m to the victims in March was retracted two months later when the Church announced that it would bankrupt the archdiocese.
Mr Garabedian said the plaintiffs had agreed to the lower figure as they wanted to put the alleged abuse behind them.
A spokeswoman for the archdiocese, Donna Morrissey, said she would not characterise the new settlement as final but added that it wished to settle the cases "in a fair and equitable manner".
Degrees of abuse
Judge Constance Sweeney is due to rule on a petition from an alleged Geoghan victim who is still a minor.
For the proposed settlement to be finalised, the judge must approve the 17-year-old's participation.
If approved, the $10m will be divided as follows:
The settlement in the Geoghan cases will not have a direct effect on other civil suits brought against the archdiocese and its leader, Cardinal Bernard Law.
Cardinal Law is accused of seeking to cover up child abuse by another defrocked priest, Paul Shanley.
Mr Shanley is on trial on charges of repeatedly raping and assaulting four young boys at a Boston church.
Another Roman Catholic priest was charged with child abuse in Boston earlier this week.
James Talbot, a Jesuit priest, was charged on Tuesday by a grand jury with raping and assaulting three students at a prestigious Boston high school during the 1970s.
The defendant worked as a teacher and wrestling coach at the school. His alleged victims were all aged between 14 and 17 at the time.
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