The Welsh rock star died peacefully on Friday night, UK time, following a complex major operation, a family statement said.
"It is with great sadness that we announce the passing of our beloved father, Philip Anthony Campbell, who passed away peacefully last night following a long and courageous battle in intensive care after a complex, major operation," said the statement, which was shared on Facebook.
"Phil was a devoted husband, a wonderful father, and a proud and loving grandfather, known affectionately as 'Bampi'.
"He was deeply loved by all who knew him and will be missed immensely. His legacy, music and the memories he created with so many will live on forever."
Motorhead was founded in 1975 by the bass player and singer Lemmy, whose real name was Ian Kilmister.
The group helped pioneer heavy metal music in Britain with a string of top 10 albums including 1980 hit Ace Of Spades, 1981's No Sleep Til Hammersmith and 1982's Ironfist.
Campbell joined the band in 1984 before it disbanded in 2015 following Lemmy's death.
He was the second-longest serving Motorhead member, after Lemmy, and went on to record music and tour with his sons, Todd, Dane and Tyla as the group Phil Campbell and The Bastard Sons.
Motorhead paid tribute to Campbell in a post shared on Instagram, describing the "wonderful" guitarist as an "enormous beam of light".
The statement said: "Phil was a wonderful guitarist, writer, performer, and musician who had Motorhead in his veins.
"He always led with his gift of guitar, and carried a great sense of humour, but most of all, Phil led with his heart. You could not be around him without a chuckle or 20, because quite simply, Phil loved life and lived it with great joy.
"There will be plenty of time for us to share stories - tales of Campbell glory - and some good jokes together; for now, please send love and positive energy to Gaynor and the boys while affording them time, space, and privacy.
"Much love and RIP Phil. The world has just lost an enormous beam of light, and we are devastated."
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