The couple, who first entered into a civil partnership seven years ago, were joined by members of the public and friends as they exchanged vows on stage with their four children at the Royal Festival Hall on London's South Bank.
Wearing a powder blue suit, Toksvig was led down the aisle by her eldest daughter to organ music played by keyboard player and songwriter Rick Wakeman on the newly-restored Royal Festival Hall organ.
The ceremony was part of the I Do To Equal Marriage event and featured music by singer and actress Sharon D Clarke, the London Gay Men's Chorus and the Fourth Choir.
The Radio 4 News Quiz presenter described the day as a "an astonishing moment in history".
In a speech, an emotional Toksvig said: "There was many a time I thought this day would never come."
Speaking of her partner, she said: "We're still crazy about each other. I can't believe my luck - look how gorgeous she is. I want a piece of paper to say she won't ever leave me."
A host of famous faces also attended, including comedian Phill Jupitus, fashion guru Mary Portas, activist Peter Tatchell, and actor Christopher Biggins.
Toksvig's friend and actress Sheila Hancock read Maya Angelou's poem, Touched by An Angel, along with Debbie's daughter - who also did a reading.
The ceremony was hosted by journalist and fellow radio presenter John McCarthy, a friend of the couple.
The couple held hands on stage as Sandi's teenage son, Theo, read out the vows.
The comedian joked that her sexuality was "just a phase" as the vows were read.
Civil partnerships were introduced in Britain in 2004. The Government has said they can be converted to marriages by the end of the year, according to Culture Secretary, Maria Miller MP.
Writing in Pink News, Ms Miller said: "I'm very much aware that there are couples who are already in a civil partnership and who may be disappointed that they will have to wait a little longer to be able to convert to a marriage."
"I'd like to reassure them that we are working hard to ensure that this process is in place by the end of year. It's taking longer because we need to introduce completely new procedures and processes."
Toksvig came out as gay in September 1994 and recounted how she was told she would never work again and had to go into hiding with her children following negative press attention.
She said: "At the time there was not a single gay woman out in public life.
"How wonderful it feels to be so much safer than 20 years ago."
Theo Toksvig-Stewart said today was the first day day that people in Britain woke up as equals.
He said: "Our mothers now have the same rights and liberties we assumed when we are born."
"Growing up I never once thought it was strange that I had two mums where everyone else had a mum and a dad. We must own our differences because that's what makes us stronger."
The audience also clapped and sang-a-long to the Gay Men's Choir's rendition of Bring Me Sunshine.
Jude Kelly, Artistic Director of the Southbank Centre, said: "It is an extraordinary thing that the rainbow flag is flying in Westminster."
She added: "It's entirely fitting that we have chosen to mark this significant event this year - both with Sandi and Debbie Toksvig renewing their vows in a public event on the first day this becomes law, and during the summer with our Festival of Love, which will culminate in a mass wedding weekend for all couples to exchange vows."
The Marriage (Same Sex Couples) Act came into force in July last year but it was not until March 13 this year when couples were able to register their intention to marry under the Act for the first time, with the first gay couples tying the knot in the early hours of this morning.
The South Bank's Festival of Love will run from June 28 to August 31, with the wedding weekend to be held on the final festival weekend of August 30 and 31.