BOSTON — The American Unitarian Association, peopled and powered by this city’s Brahmin elite, announced its presence here in 1886 with a grand and stately headquarters at the very top of Beacon Hill, right next door to the Statehouse.

If anyone doubted the denomination’s might, its next move made it clear: In 1927, strapped for space, the Unitarians finished building a new home next to the capitol on the other side, even persuading the legislature to change the street’s numbering so they could take their address with them.

But the Unitarian Universalist Association, as the denomination is now known, is selling its headquarters building, as well as two grand homes and an office building it owns in the same neighborhood. It is leaving behind the red brick sidewalks, gas streetlamps and superrich neighbors for a section of South Boston the city has designated an “innovation district,” home to up-and-coming technology and arts businesses.

Image Work continued last month on the association’s new headquarters in an “innovation district” in South Boston. Credit... Gretchen Ertl for The New York Times

The move — expected to bring tens of millions of dollars to the denomination — puts the Unitarians in increasingly familiar company. Multiple religious denominations, citing everything from diminished financial resources to a need for more contemporary office space, are simultaneously downsizing and raising money by selling longtime headquarters in expensive neighborhoods. The moves come at a time when increasing secularization in the United States is taking a toll on many religious institutions, although most say the reasons for their relocations are not solely financial.