There’s a price to pay for casting shadows on historic churches in Boston — $3 million.

That’s how much developer Boston Properties has agreed to pay into a preservation fund for historic buildings near a complex of towers it wants to build atop Back Bay Station, including Old South and Trinity churches. The company also agreed to increase its contribution to the city’s affordable housing funds by $3 million, with the money earmarked to help lower- and middle-income home buyers.

The deal comes after Old South pushed for $19 million in preservation and housing funds to make up for shadows from the $1 billion project, which sits two blocks south of the church and would, studies show, darken its ornate stained-glass windows during Sunday mornings in December. The church and its architects warned that the shadow could exacerbate water damage in the 144-year-old building, so they lobbied for a preservation fund and housing money.

Boston Properties hired its own architects, who argued that damage would be minimal, and noted their plan already met the city’s affordable housing requirements. It’s also funding improvements to Back Bay Station itself and the streets around it.

Both sides repeatedly met with city officials in recent weeks to work out a compromise, said Jon Greeley, director of development review at the Boston Planning & Development Agency.

“[The church groups] have been huge advocates and helped us make that push on housing,’’ Greeley said. “And we took very seriously the advocacy from the Mass. Historical Commission and the Boston Preservation Alliance on the buildings.’’

The agreement comes a day before the massive complex is scheduled for a vote by the Boston Planning and Development Agency board. Boston Properties declined comment Wednesday. Old South Church officials did not have an immediate comment.

Tim Logan can be reached at tim.logan@globe.com. Follow him on Twitter at @bytimlogan.