Mr Aldrin was one of the pilots on the legendary Apollo 11 spaceflight in 1969, becoming one of the first two people to walk on the moon after the mission's commander, Neil Armstrong.
The former pilot said that he and new wife Anca Faur were as "excited as eloping teenagers".
He is one of only four people alive to have walked on the moon.
Pictures from their Los Angeles ceremony were shared by Mr Aldrin on Twitter.
"On my 93rd birthday and the day I will be honoured by Living Legends of Aviation I am pleased to announce that my long-time love Dr Anca Faur and I have tied the knot," he tweeted.
Dr Faur, 63, who has a PhD in chemical engineering, is the executive vice president of Mr Aldrin's company, Buzz Aldrin Ventures.
Buzz Aldrin in the Apollo 11 Lunar Module on 20 July, 1969