"We are so grateful for the blessings from our friends and family as we commence our vows, and begin the rest of our lives together," the couple said in a statement released Sunday.
While the statement from the publicist described the rocker and actress as "married," California law does not allow marriages between same-sex couples, the Web site PlanetOut.com reports.
A new law signed last Friday by Gov. Gray Davis, however, practically grants all marriage rights to same-sex couples who register as domestic partners.
According to AP, Etheridge, 41, wore a beaded linen jacket and crepe trousers, while Michaels, 28, who starred on TV's "Popular," wore a white lace coat and a white gown.
Their platinum and diamond wedding bands were custom-made, the statement also said.
The two live in Southern California with Etheridge's daughter and son (Bailey Jean, born in 1997, and Beckett, 1998), with whom she shares custody with former lover Julie Cypher. They had the children through artificial insemination using a sperm donation from rocker David Crosby.
Etheridge and Cypher separated in 2000.
JOSH & FERGIE: ROCKED BY SCANDAL
Did he cheat with a stripper?
Married less than a year, the couple denies an Atlanta woman’s claims that she and Josh had a fling
Note that this week’s cover of PEOPLE may differ regionally
