The band has called on fans to "play Motorhead loud... play Lemmy's music LOUD" over the coming days following the singer's death
Motorhead frontman Ian "Lemmy" Kilmister has died after "a short battle with an extremely aggressive cancer".
The band confirmed that the 70-year-old died at his home while "sitting in front of his favourite video game with his family".
In a statement, Motorhead said Lemmy had learned of the cancer diagnosis on 26 December.
His fellow band members wrote: "We cannot begin to express our shock and sadness, there aren't words.
"We will say more in the coming days, but for now, please... play Motorhead loud, play Hawkwind loud, play Lemmy's music LOUD.
"Have a drink or few. Share stories. Celebrate the LIFE this lovely, wonderful man celebrated so vibrantly himself. HE WOULD WANT EXACTLY THAT."
The band's manager Todd Singerman told Sky News: "I've been with him almost 25 years and it was a half gallon of Jack Daniels a day, two/three packs of cigarettes and his other little favourites and that was a daily thing.
Singerman said Lemmy's lifestyle was unlike any other rocker: "I still always remember a great quote: Lemmy from Motorhead makes Keith Richards from the Stones look like a Golden Girl.
"This guy lived it every day and there was never a break in-between. He was the last true rock star left, if you ask me," he added.
The British group, which was first formed by Lemmy in 1975, had just celebrated their 40th anniversary.
Lemmy was famed for turning amplifiers to their maximum setting during shows, and was also renowned for his fondness of whisky and distinctive "mutton chops".
In November, Phil Taylor - a former Motorhead drummer - died aged 61 following a prolonged illness, after contributing to most of the band's best-known hits in the 1970s and 1980s, including Ace Of Spades.
Ozzy Osbourne, lead vocalist of Black Sabbath, was one of the first to pay tribute, tweeting:
Lost one of my best friends, Lemmy, today. He will be sadly missed. He was a warrior and a legend. I will see you on the other side.— Ozzy Osbourne (@OzzyOsbourne) December 29, 2015
Meanwhile, the wrestler Triple H wrote: "One life, lived your way, from the beginning, till the end. See you down the road my friend... Thank you for the gift of your sound."
A number of other stars also paid tribute to Lemmy:
Sitting here, Re-Tweeting, distracted, and wondering what I can possibly say about our utterly unique friend Lemmy's passing. Ouch. Bri— Dr. Brian May (@DrBrianMay) December 29, 2015
Lemmy, you are one of the primary reasons this band exists. We're forever grateful for all of your inspiration. RIP pic.twitter.com/WC1csn5F5x— Metallica (@Metallica) December 29, 2015
Lemmy was a true rock icon, singular in voice and spirit. Metal flags fly at half mast tonight as we salute the incomparable Ace Of Spades.— Tom Morello (@tmorello) December 29, 2015
Motorhead had been due to perform several shows across the UK in January.