Ms. Johnson said the hope was that the city would also become owner of the historical society’s building, which underwent a major renovation in 2010, by retiring its $1.9 million mortgage debt.

There may also be bit of rebranding for the historical society, including what Ms. Johnson said would probably be a name change — maybe even dropping the fusty-sounding words “historical society,” as a number of other institutions have done.

“We are going to stick to it as closely as we can, to be respectful of the mission and identity of this institution,” she said of the change. “We’re not looking to be making sweeping changes. Our goal is to expand reach and open up access.”

Ms. Schwartz, who has led the historical society since 2006, said discussions over the merger began in November as an outgrowth of existing partnerships to promote the society’s programs, like its current project relating to the history of Muslims in Brooklyn.

The arrangement will give a financial cushion to the historical society, which has an operating budget of nearly $5 million and an endowment that Ms. Johnson characterized as $1 million “at a high.” The library, whose endowment is about $50 million, has an operating budget of around $140 million.