The Duke, 33, Scotland's premier peer, married Sophie Ann Rutherford - an interior designer whose family comes from the Borders - in a traditional ceremony in front of more than 300 guests.
The wedding party then returned to Lennoxlove, owned by the duke, where guests enjoyed an acrobatic display from a Bulldog aircraft. Alexander's late father Angus, 71, the 15th Duke of Hamilton, who passed away last June, was a keen pilot and spent 11 years in the RAF.
The couple had announced their engagement last March, and were married by the Rev Neil Gardner - originally from Dunbar - at the same church where the Queen's granddaughter, Zara Phillips, will marry English rugby player Mike Tindall in July.
And little more than a week after the world had celebrated another royal marriage between the new Duke and Duchess of Cambridge in London, there was a new Countess of Cambridge in Miss Rutherford - taking the title from her husband, who is also the Earl of Cambridge.
In addition, Miss Rutherford, 34, became the Duchess of Hamilton upon wedding the Duke.
The venue had added significance as Canongate Kirk is the kirk of Holyroodhouse, and the Duke is the hereditary Keeper of the Palace of Holyroodhouse.
His best man for the wedding was his younger brother, Lord John Douglas-Hamilton, while one of the readings came from his sister Lady Ann Douglas-Hamilton.
Among the distinguished guests to attend the wedding was David Wilson, Baron Wilson of Tillyorn, Lord High Commissioner to the General Assembly of the Church of Scotland, while the Duke's uncle, James Douglas-Hamilton, Baron Selkirk of Douglas, gave a short speech and toast to the bride and groom.
Sir Garth Morrison, Lord Lieutenant of East Lothian, was a guest along with wife Gill - having attended the royal wedding in London just eight days previously.
He told the Courier: "It was a friendly, family wedding on Saturday - it wasn't a big state occasion.
"The only major disappointment about the reception was that it did happen to rain! We had plans to be in the walled garden outside but that had to be abandoned and we were in the big house.
"But it was good fun and we circled around and met people. I'm glad to say the rain stopped just in time for an acrobatics display of a Bulldog aircraft.
"At about 7pm, the Duke and Duchess were then driven away in a very handsome 1930s Rolls Royce, and I would expect there was a family party at night."
It is believed that the couple will live together on the Lennoxlove Estate.
They enjoyed a few days together in an unknown location after the wedding and plan to have a proper honeymoon later in the year.