The star told NBC's Today show: "We'll do it very quietly. But we will do it and it will be a joyous occasion."
Furnish told the Las Vegas Review-Journal the ceremony would take place in an English register office in May.
The pair have been in a civil partnership since 2005 but the law changed on Saturday to allow marriage.
"I'm very proud of Britain and the laws that we've seen come into existence since we've been together," Sir Elton said.
"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 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."
However, those already in civil partnerships are currently not able yet to convert to a marriage. The government said it hoped to rectify that before the end of the year. It is not known how that will affect the couple's plans.
Sir Elton said their civil partnership had "huge impact" on their commitment. "We didn't think it would make much difference to our relationship, but it solidified our relationship," he said.
Their civil partnership ceremony was a high-profile event held in Windsor with 650 guests. But Furnish said the wedding would be more low-key.
"With the kids, everything is different," he said. "I think what we'll do is go to a registry office in England in May, and take the boys with us, and a couple of witnesses."
The couple have two sons, Zachary who was born in 2010 and Elijah, born last year.
Furnish added: "We don't feel the need to take an extra step legally. But since we're committed for life, we feel it's really important to take that step, and take advantage of that amazing change in legislation. We all live by example."
Sir Elton John is to marry his partner David Furnish after a change in the law in England and Wales to allow same-sex weddings for the first time.