Crowds are arriving in Windsor, while hundreds more camped out overnight to secure the best viewing spot.
Prince Harry has been made the Duke of Sussex by his grandmother the Queen, Buckingham Palace announced.
The couple will wed at noon at St George’s Chapel in Windsor Castle, before travelling through the town.
In her vows, Ms Markle will not promise to “obey” her husband and Prince Harry has chosen to have a wedding ring.
Prince Charles will walk Ms Markle down the aisle, after her father, Thomas, was unable to attend for health reasons.
On the eve of their wedding, Prince Harry told crowds in Windsor he was feeling “relaxed” and Ms Markle said she was feeling “wonderful”.
Ahead of the marriage, Prince Harry was given the title Duke of Sussex, meaning Ms Markle will become a duchess once the couple marry.
The previous Duke of Sussex was Prince Augustus Frederick, the sixth son and ninth child of George III.
Prince Harry, who is sixth in line to the throne, also received the titles Earl of Dumbarton and Baron Kilkeel.
Analysis by Jonny Dymond
This is a very different royal wedding.
It’s different because of the style of the arrangements for the day itself.
From small things, like the cake (not a traditional big heavy fruitcake covered with bullet-proof icing), to bigger things, like a gospel choir performing at the service.
To more remarkable decisions, like the invitation to 1,200 members of the public to enjoy the occasion in the grounds of Windsor Castle.
After the death in 1997 of Prince Harry’s mother, Diana, Princess of Wales, she was described by the-then Prime Minister Tony Blair as “the people’s princess”.
This may not be “the people’s wedding”, but it is about as close to it as any royal wedding has got.
Crowds of well-wishers and the world’s media have been gathering in Windsor in the week leading up to the big day.
As many as 100,000 people are expected to line the town’s streets.
Nicky and Matt Pruner, from the US, extended their holiday in the UK to be in Windsor for the wedding.
Nicky Pruner, 62, said: “I camped out all night at Kate and William’s wedding and I said I would never do it again – and here I am.”
And corks were popping early for some – like Rachael Carter-Eagleton from London who had her first glass of bubbly just after 08:00.
“I’m just so happy for Harry,” she said. “I can’t wait to see what Meghan’s wearing.”
Six hundred guests will watch the wedding, officiated by the Archbishop of Canterbury, Justin Welby, in St George’s chapel.