The 34-year-old actress said "yes" when Bob Ritchie - Kid Rock's real name - proposed on Thursday night outdoors in the Las Vegas desert.
Anderson's publicist Marleah Leslie says she is elated. No wedding date has been set.
The couple began dating in April 2001, when they met backstage at VH1's diva salute to Aretha Franklin at Radio City Music Hall in New York City.
It will be the second marriage for Anderson, who is locked in a child custody battle with ex-husband Tommy Lee over sons Brandon and Dylan.
Last month, Anderson claimed she had contracted the potentially fatal hepatitis C by sharing a tattoo needle with Lee.
The former Motley Crue drummer insists, however, that he has never had the disease.
Anderson said she has been undergoing outpatient treatment at a Los Angeles medical centre.
It will be the first marriage for 31-year-old Rock, who has a young son he raises with the help of his sister in northern Michigan.
