Bruce, who is also governor of Edinburgh Castle, married Stephen Knott at St John's Episcopal Church on Saturday afternoon.
Sharing the news on Twitter, the descendant of Robert the Bruce wrote: “This would not have been possible in [the] British Army I joined in 1979.
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“Attitudes change but love is constant.”
Bruce was born in Winchester and brought up in Hampshire in south-east England, but spent much of his childhood in the north of the Scottish Highlands, where his parents owned the Sallachy Estate near the village of Lairg.
He received several military awards throughout his long and distinguished career in the armed forces.
Bruce has also worked as a historical adviser on hit TV shows and films, including Downton Abbey and The King's Speech, and recorded a conversation with Queen Elizabeth II for the BBC in 2017.