The 33-year-old shared pictures from her special day on Instagram on Sunday, including a snap of her stunning lace gown, and wrote: "#AboutLastNight.Over the moon to announce I'm a Mrs today! #Sundaylove."
According to the New York Post's gossip column Page Six, Keith and his model wife Patti Hansen hired out the Lachat Town Farm in Weston, Connecticut for the celebrations.
A source told the publication that guests were shuttled from Keith's home nearby to the venue in golf carts.
"Guests walked or took golf carts from Keith's home where the wedding party kicked things off with loud music," the insider said.
At the venue, a 42-acre farm, Alexandra and Jacques tied the knot in a white marquee surrounded by fairy lights. As the reception got underway, guests, who dined on lamb, were heard cheering following the speeches and toasts.
Among the celebrity guests at the ceremony were Keith's Rolling Stones bandmates Ronnie Wood and Charlie Watts, as well as Ronnie's daughter Leah Wood. Mick Jagger - the fourth member of the group - wasn't in attendance.
Alexandra and visual artist Jacques got engaged in January, with Patti celebrating the news with fans by sharing a picture of the happy couple on Instagram.
"She said yes ! @officialalexandrarichards," Alexandra's proud mother captioned the shot. "mom and dad love Jacques and we could not be happier for our Alexandra... happy new year!! With so much love".
The marriage is Alexandra's first.