Nicola Sturgeon tweeted: “Many congratulations to the happy couple!”, along with a picture of Harry and Meghan sharing their first kiss as husband and wife.
Scottish Conservative leader Ruth Davidson praised a “wonderful sermon, fabulous choirs and a young couple just looking smiley and happy”.
Scottish Labour leader Richard Leonard also sent his congratulations to the Duke and Duchess of Sussex.
Events in Scotland were low-key with just a handful of street parties taking place, including one in Buckstone Road in the capital.
Residents in Markle in East Lothian, a tiny Scottish village which shares its name with Prince Harry’s bride, held an outdoor party and barbecue in honour of the event.
Outside the Palace of Holyroodhouse in Edinburgh visitors offered their best wished to the newlyweds.
Jenny Edwards, 58, from Birmingham, said: “We watched the vows and it was very emotional. Diana would been proud of her boys, they are lovely young men.
“It was absolutely amazing. It was simple just right for them. We really enjoyed it.”
Carole Murienne, 42, from Paris, said: “It’s very nice for us the French people, we don’t have royals anymore, so I’m very curious.
“I think it’s an amazing wedding, it’s really a dream for this girl Meghan. It’s a dream story.”
Anne Drew, 72, from West Virginia, USA, said: “I’m originally from London and I think this is great that he’s marrying an American because I’m an American citizen now.
“I think she’s lovely and I think they’re very well suited for their humanitarian work and I’m very happy about it, I think she’s brought a breath of fresh air to the royal family.”
Several hotels and stately homes held events, such as the National Trust for Scotland property Haddo House in Aberdeenshire which held an afternoon tea, with live BBC coverage of the wedding.
At Balmoral, the royal family’s Scottish home, every visitor received a free special Royal Wedding Cup Cake.
Hotels including Fairmont St Andrews and the Blythswood Square Hotel in Glasgow held celebratory afternoon teas, while the Royal Yacht Britannia’s Royal Deck Tea Room served a special menu of the Royal couple’s “favourite dishes” including roast chicken sandwiches and lemon and elderflower cake - based on the couple’s choice of wedding cake.
Scotland’s Theme Park, offered free entry with anyone named Harry and Meghan - with all spellings of the bride’s name accepted.
There were 311 couples set to get married across Scotland on Saturday, according to the National Records of Scotland.