"We were joined in holy matrimony in a small private ceremony in Los Angeles & are as excited as eloping teenagers," Aldrin said on Twitter.
The marriage to Faur is his fourth.
The intense fame generated by the Apollo 11 mission 54 years ago overwhelmed Aldrin after he returned to Earth.
The former fighter pilot suffered from depression and alcoholism, but ultimately came to terms with his fame and has been known since for his public appearances. He is also the author of nine books and remains an advocate for human space exploration.