The commemorative plaque marks the achievements of the author of Ulster's Solemn League and Covenant, which was drawn up just under 10 years before the partition of Ireland and the establishment of Northern Ireland.
The Covenant was a pledge signed by almost half a million unionists to oppose Home Rule in Ireland "by all means necessary", and was signed on September 28, 1912.
The first signatory was Sir Edward Carson, then leader of the Ulster Unionist Party, whose statue stands at Stormont to this day.
The plaque, bestowed by the Ulster History Circle, was erected on the side of the Sinclair Seamen's Church, which was built by Thomas Sinclair's uncle, John Sinclair, in 1857.
Speaking at the event, Mrs Foster said it was a privilege to honour the life of "this remarkable man" who she said had an "unquestionable influence on Northern Ireland's history".
"As author of the Ulster Covenant in 1912, during what was a turbulent time in Northern Ireland's creation, Thomas Sinclair undoubtedly created a legacy that lives on today," she added. "He will long be remembered for his important contribution to business, politics and academia at every level at that time.
"I'm delighted to be joined here today with descendants of Thomas Sinclair and to unveil this most deserved plaque in his memory."
The unveiling was part of a series of projects being launched at an event at Sinclair Seamen's Church.
The Ulster-Scots Agency also used to occasion to launch the book Thomas Sinclair, Ulster's Most Prominent Citizen, in partnership with the Ulster Historical Foundation.
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