As most Australians were sleeping, Alan Wright and Joel Player were celebrating history with the nation's first same-sex wedding ceremonies held at one minute past midnight in Canberra.

The threat of the High Court striking down the ACT's same-sex marriage laws next week was to have been momentarily set aside as they exchanged vows and rejoiced with friends beneath the 55 bronze bells of the National Carillon at Lake Burley Griffin at 12.01am.

"To have it finally legalised, it's a big step for us in our relationship, so we're just wanting to get it done," Mr Player said.

Mr Wright, 34, said the decision to get married in the middle of the night was made not for a grab at history, but to fulfil the words of their celebrant Sharyn Gunn, who performed the couple's commitment ceremony - which they consider the start of their marriage - four years ago.