The chart-topper wore a traditional bespoke wedding gown with a veil and train designed by Natacha Ramsay-Levi for Chloe, while Mr Jopling opted for a suit from Savile Row tailors Huntsman.
The pair exited the minster after tying the knot, pausing on the steps to kiss before leaving in in the same blue Volkswagen campervan that delivered them to the service on Saturday afternoon.
A reception was then held at Castle Howard, the stately home near Malton, North Yorkshire, made famous by the 1980s TV adaptation of Brideshead Revisited.
The lavish event saw an extensive guest list of royals, actors, musicians and TV personalities including the Duchess of York and her daughters, Princesses Beatrice and Eugenie.
Goulding, who was flanked by five bridesmaids and two flower girls, had arrived some 25 minutes late to the service.
She was greeted by Archbishop of York Dr John Sentamu, who led her into the minster.
Singer Katy Perry arrived with her Hollywood star boyfriend Orlando Bloom, who was in London earlier this week to promote his new Amazon series with Cara Delevingne, Carnival Row.
Also in attendance were singer James Blunt, actress Sienna Miller, comic Jimmy Carr and artist Tracey Emin.
The groom, 27, gave a thumbs-up to waiting guests on his arrival. He was cheered by the crowds and greeted with an announcement by York’s town crier.
Several hundred people had gathered outside the south door of the minster waiting for the bride and any celebrity arrivals.
Goulding performed at the Duke and Duchess of Cambridge’s wedding party in 2011 and, with her fiance, was a guest at Princess Eugenie’s marriage last October.
Goulding and Mr Jopling have been together for more than two years and announced their engagement with a formal notice in The Times a year ago.
Mr Jopling’s father is the Honorable Nicholas Jopling, of Frickley Hall, near Doncaster, South Yorkshire.
After the wedding was formally announced last year, Goulding said she was looking forward to being a “loved-up wife”.