The 67-year-old singer posted a picture on photo-sharing website Instagram of himself and Furnish in blue suits brandishing a pen as they signed a form.
"That's the legal bit done. Now on to the ceremony!" said the caption.
A fleet of luxury cars whisked the A-list guests through the gates of the couple's estate in Windsor, west of London, close to the castle where Queen Elizabeth II spends much of her time.
Former footballer Beckham arrived with his children and wife Victoria while comedian David Walliams was spotted with model wife Lara Stone.
Notting Hill star Hugh Grant made an eye-catching entrance in a Ferrari, with all guests arriving between 12:00 and 13:00 local time (12:00-13:00 GMT).
The Rocket Man musician earlier posted a picture of an invitation on his Instagram page, with the words "Sir Elton John and David Furnish request the pleasure of your company to celebrate their wedding on Sunday the 21st December" written on a background of red roses.
It was among the first posts to his newly opened Instagram account.
Other pictures show a view of the couple's estate under the words "Good morning! Nice day for a wedding," and the couple's three-year-old son Zachary holding a teddy bear while they exchange vows.
Both Zachary and the couple's other son, Elijah, 23 months, were ring bearers.
The photographs showed at least 50 guests - reported to include Ed Sheeran, Elizabeth Hurley and Ozzy and Sharon Osbourne - sat in what appeared to be the estate's gallery, in front of art works thought to be by Gilbert & George and Damien Hirst.
Guest Brooklyn Beckham, eldest son of David and Victoria, later posted a photograph of the wedding lunch menu, which included a wild mushroom soup and truffle cream starter followed by beef short rib and caramelised onion pie with roasted potatoes and parsnips in horseradish butter.
Dessert was warm chocolate pudding and vanilla ice cream with wedding cake to follow.
Singer 'proud of British law'
The singer voiced pride that England and Wales began allowing same-sex marriage in March. Scotland followed suit last week.
John and Furnish - who divide their time between England, Beverly Hills, Atlanta, Venice and Nice in the south of France - entered a civil partnership soon after the institution began in Britain in 2005 and have now been together for 21 years.
"I'm very proud of Britain and the laws that we've seen come into existence since we've been together," John told US TV network NBC in March.
"Having our civil partnership was an incredible breakthrough for people that have campaigned for a long time - through the '60s and the '50s in England when it was so hard to be gay and hard to be open about it. And it was a criminal act.
"So for this legislation [gay marriage] to come through is joyous, and we should celebrate it. We shouldn't just say, 'Oh, well we have a civil partnership. We're not going to bother to get married.' We will get married," he said.
The 2005 celebration was a much grander affair, with 650 guests invited.
"Sir Elton", who was knighted in 1998, was ranked number four in the most recent Sunday Times newspaper Rich List of British and Irish musicians, with a personal wealth estimated at £240m.
Early in his career, John hid his sexuality and married a woman. He later became an advocate for gay rights and has been active in the fight against Aids.