Her death was announced on Wednesday on the band's social media accounts. No cause of death or other details were provided, but a family statement said she died peacefully in hospital after a short illness with family by her side.
"She was truly one-of-a-kind, special and talented beyond measure," the band said.
In a note on Instagram, bandmate Stevie Nicks said: "A few hours ago I was told that my best friend in the whole world since the first day of 1975, had passed away."
She said one song had been "swirling around" in her head since she found out McVie was sick, quoting the lyrics to HAIM's Hallelujah: "I had a best friend/But she has come to pass."
McVie was a steady presence in a band known for its frequent line-up changes and volatile personalities, notably fellow singer-songwriters Nicks and Lindsey Buckingham. Her death is the first among Fleetwood Mac's most famous incarnation of McVie, Nicks, Buckingham, drummer Mick Fleetwood and bassist John McVie, Christine's ex-husband.
Fleetwood Mac began as a London blues band in the 1960s and evolved into one of the defining makers of 1970s California pop-rock. During its peak commercial years of 1975-80, the band sold tens of millions of records and fascinated fans as it transformed personal battles into melodic, compelling songs. The McVies' break-up - along with the split of Nicks and Buckingham - was famously documented on the 1977 release Rumours, among the best-selling albums ever.
"I was supposedly like the Mother Teresa who would hang out with everybody or just try and (keep) everything nice and cool and relaxed," McVie told Rolling Stone earlier this year. "But they were great people; they were great friends."
Fleetwood Mac was inducted into the Rock and Roll Hall of Fame in 1998. The group's many other hit singles included Nicks' Dreams, Buckingham's Go Your Own Way and McVie's Little Lies. One of McVie's most beloved works, the thoughtful ballad Songbird, was a showcase for her in concert and covered by Willie Nelson, among others.
The mid-tempo rocker Don't Stop, inspired by the end of her marriage, would gain unexpected political relevance when Bill Clinton adopted the song - and its "Don't stop thinking about tomorrow" refrain - as a theme to his 1992 presidential run.
McVie's two marriages, to John McVie and Eduardo Quintela, ended in divorce. Her boyfriends included the Beach Boys' Dennis Wilson, about whom she wrote Only Over You.
McVie, was born Christine Anne Perfect in Bouth, Lancashire. Her father was a violinist and music teacher and her grandfather played organ at Westminster Abbey. She learned to play piano but set aside her classical training once she heard early rock records by Fats Domino and others.
She befriended members of Britain's emerging blues scene while studying at the Moseley School of Art and, in her 20s, joined the band Chicken Shack. Among the rival bands she admired was Fleetwood Mac, which then featured the talents of blues guitarist Peter Green along with the rhythm section of Fleetwood and John McVie. By 1970, she had joined the group and married John McVie.
Few bands succeeded as well as Fleetwood Mac, which has sold well over 100 million records, against such long odds. Green was among the many performers who left the group, and at times Fleetwood Mac seemed on the verge of ending or fading away before being rescued by unexpected returns and interventions.
In the mid-1970s, Fleetwood Mac was down to just three members: Fleetwood and the two McVies. While in Los Angeles, Fleetwood became impressed with young duo from California, Buckingham and Nicks. He planned to ask just Buckingham to join, but the guitarist insisted the band also include his girlfriend Nicks.
The new line-up proved ideal. Nicks and Christine McVie formed a lasting friendship, and the harmonies and music-making of Nicks, Buckingham and Christine McVie ensured that such albums as Fleetwood Mac, Rumours and Mirage had a variety of songwriting and vocal styles.
But the group's success also led to inevitable conflicts and the desire for solo work. In the following decades, Nicks became a star in her own right with such solo albums as Bella Donna and both Buckingham and Christine McVie departed for years, only to eventually come back.
The pair recorded the 2017 album Lindsey Buckingham/Christine McVie. She previously released the solo records Christine Perfect, Christine McVie and In the Meantime.
More recently, Buckingham was kicked out, replaced on tour by Mike Campbell and Neil Finn.
An anthology of McVie's solo work, Songbird, was released earlier this year.
