Miss Middleton is wearing an ivory and lace gown designed by Sarah Burton at Alexander McQueen.
Some 1,900 guests watched the couple exchange their vows, with many millions watching at home. The service is expected to finish at 1215 BST.
Thousands of people are lining the procession route the couple will take to Buckingham Palace after the service.
Despite the risk of showers, the pair will travel in an open-topped 1902 State Landau carriage for the procession, which was used by Prince William parents for their wedding in 1981.
The day has started off dry and cloudy in London but the Met Office says there is a risk of heavy showers developing later on. Temperatures in the capital are expected to reach a high of 19C (66F) in the afternoon.
The prince is wearing the red tunic of an Irish Guards colonel - his most senior honorary appointment - but the bride's dress design is being kept secret.
Prince William has been given the title of the Duke of Cambridge by the Queen, and Miss Middleton will become Her Royal Highness the Duchess of Cambridge on their marriage.
The prince has also became the Earl of Strathearn and Baron Carrickfergus, which means Miss Middleton will become the Countess of Strathearn and Baroness Carrickfergus.
Street parties
Well-known faces have been spotted at Westminster Abbey, including singer-songwriter Sir Elton John and his partner David Furnish, former England rugby coach Sir Clive Woodward, and former England football captain David Beckham and his wife Victoria.
Actor Rowan Atkinson, a close friend of Prince Charles, Prince Harry's friend Chelsy Davy and film director Guy Ritchie have also arrived.
UK Prime Minister David Cameron and his wife Samantha, Australian prime minister Julia Gillard, former British PM Sir John Major, and current Home Secretary Theresa May are among the politicians present. Mr Cameron did not cause an etiquette upset and wore a morning suit despite initially suggesting he might not.
BNewsworld reporters at the scene estimated between 3,000-5,000 people had been camping overnight in the Mall and around Westminster Abbey.
For those lining the route, large speakers will broadcast the wedding service, and it is anticipated the event will be watched by hundreds of millions of people worldwide on television.
The busy schedule began when guests start arriving at the Abbey from 0815 BST. Many had been queuing before the Great North Door opened
A Rolls-Royce picked up Miss Middleton at the Goring Hotel, where the Middleton family is staying, at 1050BST. Prince William travelled to the Abbey with his brother and best man in a Bentley
Out of the 1,900 guests at the Abbey, 1,000 are friends and family, who have been given some of the best seats in the house. The others include overseas royals, politicians from home and abroad, military personnel and representatives from various faiths and charities
After the service, the newlyweds will travel in an open-topped carriage for the 15-minute journey from Westminster Abbey to Buckingham Palace, past some of London's most famous landmarks, including the Houses of Parliament, Big Ben and Horse Guards Parade. The couple will appear on the balcony at about 1325 BST
Thousands of street parties are being held around the UK, and big screens have been put up in many towns and cities. The BNewsworld will be bringing viewers and listeners comprehensive coverage across TV, radio and online, both in the UK and around the world
5,000 officers are on duty, with more than 900 along the wedding route. Most are in uniform, but some will be in plain clothes, mixing with the crowd
About two square miles of central London have been closed to traffic.
The Archbishop of Canterbury, the Most Reverend Rowan Williams, will conduct the wedding ceremony, which will see Miss Middleton vow to "love, comfort, honour and keep" Prince William but not to obey him.
Dr Williams told the BNewsworld he was "very excited" about the wedding.
"They strike me as deeply sensible, realistic, but also people with strong ideals about marriage and about other things," he said.
The couple did not want a "great kind of all-singing, all-dancing extravaganza", he added.
"They've wanted something simple and clear, but they've also wanted something with obvious traditional routes and associations, and I think that's what's really shaped what's going to happen today," he said.
Royal officials said William and Kate have been involved in planning their wedding day, from the music at the ceremony to the flowers and the cake.
Inside Westminster Abbey, an avenue of trees line the red carpet leading up to the altar.
Some 650 guests have been invited to the palace for a buffet lunch and about 300 close friends and relatives will stay on for formal black tie dinner and disco in the evening.
But the Queen and the Duke of Edinburgh will leave for a weekend away after hosting the lunchtime reception and will miss Prince Harry's best man speech and Michael Middleton's father of the bride address.
The couple have chosen royal warrant holders Wartski to make the wedding ring for Miss Middleton. Following a long tradition of royal weddings, it has been fashioned by the Bangor-founded firm from Welsh gold given to Prince William by the Queen.
In their official wedding programme released on Thursday, the royal couple said: "The affection shown to us by so many people during our engagement has been incredibly moving, and has touched us both deeply."
Prince William's choice of a military uniform for his wedding is something of a surprise, royal watchers say. As a search and rescue helicopter pilot in the Royal Air Force, many had predicted he would wear his blue flight lieutenant's uniform.
However, as an honorary colonel of the Irish Guards infantry regiment, he has opted to wear the red tunic and forage cap, fitted by military and civilian tailors Kashket and Partners.
Prince Harry is a captain in the Household Cavalry's Blues and Royals regiment and is wearing his uniform, while Prince Charles will be in his Royal Navy admiral's outfit.
The bride will walk up the aisle to coronation anthem I Was Glad, by Sir Charles Hubert Hastings Parry, from Psalm 122.
It was composed for the crowning of Prince William's great-great-great grandfather, Edward VII, at Westminster Abbey in 1902.
The couple have chosen to use the Series One (1966) Book of Common Prayer ceremony.
Classical compositions by Elgar, Britten and Vaughan Williams will feature during the ceremony, alongside the hymn Jerusalem and the English melody Greensleeves.
The Prince of Wales and the Duchess of Cornwall, Prince Harry, Miss Middleton's parents - Carole and Michael Middleton - her sister Pippa and her brother James will all act as witnesses and sign the marriage registers.
James Middleton will also give The Lesson, reading Romans 12: 1-2, 9-18.
