In her vows, Ms Markle did not promise to “obey” her husband, while the prince broke with royal tradition by choosing to wear a wedding ring.
Prince Harry’s ring is a platinum band with a textured finish and Ms Markle’s has been made from a piece of Welsh gold.
Lady Jane Fellowes, the sister of Prince Harry’s late mother, Diana, Princess of Wales, gave a reading.
Karen Gibson and The Kingdom Choir performed Ben E King’s soul classic Stand By Me during the service.
As the bride and groom signed the register, 19-year-old cellist Sheku Kanneh-Mason – who won the 2016 BBC’s Young Musician – performed three pieces – by Faure, Schubert and Maria Theresia von Paradis, with musicians from the BBC National Orchestra of Wales, the English Chamber Orchestra and the Philharmonia.
The gospel choir also performed Etta James’ uplifting version of Amen/This Little Light of Mine as the newlyweds left the chapel.
The duke and duchess will travel through Windsor along a route lined by up to 100,000 well-wishers.
All 600 guests will then attend a lunchtime reception at St George’s Hall, which is being given by the Queen.
During this reception, Ms Markle will reportedly break with tradition for royal brides and make a speech.
During the service, the couple pledged themselves to one another, saying: “For better, for worse, for richer, for poorer, in sickness and in health, to love and to cherish, till death us do part.”
‘Power in love’
The Most Rev Bishop Michael Curry, the 27th presiding bishop and primate of the Episcopal Church, from Chicago, gave an address, and the Rt Rev David Conner, Dean of Windsor, conducted the service.
“There’s power, power in love. If you don’t believe me think about a time when you first fell in love. The whole world seemed to centre around you and your beloved. Well… there’s power, power in love,” Bishop Curry said in his address.