The Royal Family and celebrities are among the 850 guests at the ceremony.
The ninth in line to the throne was given away by her father, Prince Andrew – watched by her grandmother, the Queen.
Prince Philip, Eugenie’s mother, the Duchess of York, and her sister Beatrice, are also attending, along with crowds of well-wishers outside.
Around 1,200 members of the public selected by ballot are listening to a live broadcast in the castle grounds, and thousands are watching outside in extremely windy conditions.
The wedding is being screened in full on ITV as part of a three-hour special of the daily magazine show, This Morning.
The 28-year-old and drinks executive Jack Brooksbank, 32, are tying the knot at St George’s Chapel – where Prince Harry and Meghan Markle married in May.
The couple met when skiing in Switzerland in 2010.
BBC royal correspondent Jonny Dymond said there were “lots of smiles and lots of nerves from the couple”.
He said the bride kept breaking into a broad smile and the groom was delighted, but “both of them a little nervous too, their hands shaking together before they took their vows”.
The Duke and Duchess of Cambridge’s children, Prince George and Princess Charlotte, are taking on pageboy and bridesmaid roles.
The other bridesmaids are Mia Tindall – daughter of Zara and Mike Tindall – Mia’s cousins Savannah and Isla, Eugenie’s goddaughter Maud Windsor and Robbie Williams’ daughter, Theodora.
The other pageboy is Louis de Givenchy, six, the son of friends.
Eugenie’s sister, Princess Beatrice, is maid of honour. Mr Brooksbank has chosen his brother, Thomas, as best man.
Among the celebrities sharing their special day are model Cara Delevingne, singer Robbie Williams, comedian Jimmy Carr and David Emanuel – who designed Princess Diana’s wedding dress.
Italian tenor Andrea Bocelli performed two pieces during the ceremony, which also featured members of the Royal Philharmonic Orchestra.
The Archbishop of York, Dr John Sentamu, has also prepared a personal prayer.
Dean of Windsor David Conner is officiating.
The couple will travel from St George’s Chapel along Windsor High Street and the Long Walk, before an afternoon reception hosted by the Queen in St George’s Hall at the castle.
An evening party will take place at the York family home, the Royal Lodge, in Windsor Great Park.
The families are paying for the private aspects of the wedding.
However, republican campaigners say taxpayers face an estimated £2m security bill.
The campaign group Republic argues that as Princess Eugenie, the ninth in line to the throne, does not carry out public duties, the families should foot the bill.
Buckingham Palace says this is a matter for the police.