The singer told NBC's Today show that he wants to celebrate "very quietly," and added: "It will be a joyous occasion and we will have our children."
The two men, who have been in a civil partnership since 2005, have two children.
In quotes released on NBC's website Monday, the singer said: "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."
Same-sex marriages were allowed for the first time in Britain Saturday, when a new marriage law came into effect.