Nicks lamented the loss of her “best friend in the whole world”, while Fleetwood said part of his heart “flew away” after the news.
McVie’s family confirmed her death on Wednesday after a short illness.
Fleetwood Mac released a joint statement, though Fleetwood and Nicks later posted their own personal messages on social media.
“This is a day when my dear, dear friend Christine McVie has gone on the run, leaving us earthbound humans to listen with bated breath to the sounds of that ‘songbird’, to remind everyone that love is everywhere. around us is to reach out and touch in this precious life bestowed on us,” wrote Fleetwood.
“Part of my heart flew away today… I will miss everything about you Christine McVie.
“Memories abound…they fly to me. Mike Fleetwood.”
Nicks said she hadn’t known McVie was ill until Saturday night and wanted to visit her in London.
“A few hours ago I was informed that my best friend in the entire world had passed away since the first day of 1975,” she wrote in a heartfelt post on Instagram.
“I didn’t even know she was sick…until late Saturday night. I wanted to be in London, I wanted to go to London – but we were told to wait.
“So since Saturday, one song has been swirling through my head, over and over. I thought maybe I could sing it to her, so I’m singing it to her now.
“I always knew I would need these words one day… That’s all I can do now.”
Nicks then shared the handwritten lyrics to Haim’s song Hallelujah, adding: “See you on the other side, my love. Do not forget about me. Always, Steve.
British-American rock band Fleetwood Mac formed in London in 1967 and have sold over 100 million records worldwide, making them one of the most successful groups in history.
Their most famous songs are Dreams, Go Your Own Way and Everywhere.
Despite its tumultuous history, Fleetwood Mac became one of the best-known rock bands of the 1970s and 1980s, consisting of Mick Fleetwood, Christine and John McVie, as well as Lindsey Buckingham and Nicks.
Perhaps their most famous album, Rumors – released in 1977, became one of the best-selling of all time and featured hits such as Second Hand News and You Make Loving Fun.
In addition to several multi-platinum tracks, the record has sold over 40 million copies worldwide.
A statement from the band on Twitter described McVie as “truly unique, special and extremely talented”.
“There are no words to describe our sadness at the passing of Christine McVie. She was truly one-of-a-kind, special and extremely talented,” the statement read.
“She was the best musician anyone could have in their band and the best friend anyone could have in their life.
“We were so lucky to have a life with her. Individually and together we have deeply cherished Christine and are thankful for the wonderful memories we have. She will be missed so much.”
Singer-songwriter and keyboardist McVie wrote Songbird, one of the band’s most famous songs, as well as You Make Loving Fun, Oh Daddy and Little Lies.
Duran Duran bassist John Taylor said McVie had “exuded both purity and brutality in equal measure”.
“So sad to hear about Christine McVie, an artist I held dear and close to my heart,” Taylor posted from the band’s account.
“As one of the greatest songwriters, singers and band members of all time, she exuded both purity and sass in equal measure, bringing light to the music of the 1970s. REST IN PEACE. – Jan.”
Another tribute came from American musician Sheryl Crow, who wrote, “I am so sad to hear that Christine McVie is going to heaven.
“The world feels strange without her here. What a legend and an icon and a wonderful human being. REST IN PEACE.”
In 1970, McVie released her first solo album, Christine Perfect, after her maiden name. In an interview this year, she told Uncut magazine, “It might have some good songs on it.”
It took McVie another 14 years to release a follow-up solo album – titled Christine McVie – before releasing another album in 2004.
In June of this year, the singer-songwriter released another album titled Songbird, a collection of songs taken from two of her previous solo albums.
She was one of eight members of the band inducted into the Rock & Roll Hall of Fame in 1998.
McVie left the band in 1998 after nearly three decades, but rejoined in 2014 when a one-off gig at the O2 rekindled her love of performing.
She told The Guardian at the time: “It was amazing, like I had never been away. I climbed back on and there they were, the same old faces on stage.”
In 2017, she appeared on BBC Radio 4’s Desert Island Discs, revealing that she had withdrawn from the world and developed agoraphobia after leaving the band and moving from California to Kent.
McVie’s death comes two years after Fleetwood Mac co-founder Peter Green died aged 73.
A statement from her family said: “It is with a heavy heart that we inform you of Christine’s death. She passed away peacefully in hospital this morning, Wednesday, November 30, 2022 after a short illness.
“She was in the company of her family. We kindly ask that you respect the family’s privacy at this most painful time and we would like everyone to hold Christine in their hearts and remember the life of an incredible human being and a respected musician who was universally loved.