The couple will tie the knot at St George's Chapel, Windsor Castle, at 12 noon on Saturday 19 May, followed by a carriage procession through the town.
Kensington Palace released an update saying that the pair are "hugely grateful for the many good wishes they have received since announcing their engagement".
"They are very much looking forward to the day and to being able to share their celebrations with the public," it added.
The wedding is due to take place on the same day as the FA Cup Final at Wembley Stadium.
But fans of both football and the Royals can rest easy as a clash is now highly unlikely - recent cup finals have kicked off at 5.30pm and the wedding ceremony is taking place five-and-a-half hours before.
As president of the Football Association, the Duke of Cambridge usually attends the FA Cup Final and presents the trophy.
But this year, Prince William - who is tipped to be Harry's best man - looks likely to be otherwise engaged with wedding duties.
It has also been confirmed that the Archbishop of Canterbury, Justin Welby, will marry the couple.
The Rt Rev David Connor, Dean of Windsor, will also conduct the service at the 15th century historic chapel.
Arrangements for the day include a procession at 1pm when the newly married couple will leave the chapel, go through the castle gates, and follow a loop back around the town.
The route includes Castle Hill, High Street, Sheet Street, Kings Road, Albert Road and Long Walk.
The Palace said that Harry and Meghan "hope this short journey will provide an opportunity for more people to come together around Windsor and to enjoy the atmosphere of this special day".
There will then be a reception at St George's Hall for the pair and their congregation guests.
Later Prince Charles will give a private evening reception for the couple and their close friends and family.
Alastair Bruce, royal commentator, said: "A wedding is a wedding but for the Royal Family there is always an element of public interest.
"The structure of putting together a ceremony that follows a traditional path is very much what is kind of expected.
"So I think that the planning here has followed some of the traditions of the past and using the shape of the castle both to have a private event and the streets outside to make that public element work so well."
Roya Nikkhah, royal correspondent for the Sunday Times, said the wedding is expected to have much more of a "showbusiness" feel.
"I've reported that Meghan is going to give a speech at her wedding that is very different from what we have seen before.
"I think it will have a slightly more modern twist than previous royal weddings and we are seeing that with this update with the carriage process to involve the public.
"That is a new departure."
Harry and Meghan have chosen a Saturday, which is also against tradition, as royal weddings usually take place on a week day.
Already shops in Windsor are making plans. Aamir Bukhri, owner of the Chippy of Windsor, said he was planning to decorate the front of his shop.
"Windsor has just gone to a different stage, it is reborn, it's a new introduction," he said.
"We are going to put up British flags, some pictures as well outside, and some nice flowers, and some bunting.
"We are hoping this summer will be very busy here and we are feeling that because a lot of people are already coming in and talking about (the wedding)."