Premier Stephen McNeil was scheduled to hold a news conference to discuss the agreement later Tuesday.
"We're not done yet — there are still some legal steps in the process. But this is a significant step forward in the right direction," McNeil said in a statement announcing the agreement.
"Former residents have been through a lot and for their sake, it's good that we're closer to a resolution."
Court documents will be filed later Tuesday detailing the lump sum settlement to be disbursed by lawyers representing the former residents, McNeil added.
McNeil said in November that his Liberal government wanted to negotiate a settlement with the plaintiffs after they launched a class-action lawsuit against the province.
About 150 former residents allege they were sexually, physically and psychologically abused by staff at the home over a 50-year period up until the 1980s. Their class-action lawsuit was certified by the Nova Scotia Supreme Court in December, though the allegations have not been tested in court.
The previous NDP government fought the lawsuit in the courts before being defeated in October's provincial election, arguing that some of the allegations are based on speculation or hearsay.
The agreement announced Tuesday is scheduled to go before the province's Supreme Court for preliminary approval on Friday, with final court approval tentatively set for July 7. The deal is expected to be finalized by the end of September, McNeil said.
After the settlement is reached, the government will begin developing terms of reference for a process to give former residents an opportunity to publicly share their stories, he added.
In April 2013, the Home for Colored Children agreed to pay a $5-million settlement to about 140 plaintiffs after they filed a class-action lawsuit against the orphanage.