The musician was found dead at his home in Groton, Massachusetts, on Tuesday.
Local police, who had been called to the property to check on his welfare, attributed his death to natural causes.
Founded in 1967, The J Geils Band released 11 studio albums, among them the US chart-topping Freeze-Frame, before breaking up in 1985.
Centrefold, their biggest hit, topped the US charts for six weeks in 1982 and reached number three in the UK.
The song is known for its catchy intro and its chorus: "My blood runs cold/My memory has just been sold/My angel is the centrefold/Angel is the centrefold."
The band reunited in recent years for occasional appearances, including one at the Boston Strong concert that took place in the wake of the Boston Marathon bombings in 2013.
In later life, Geils released a series of jazz albums while indulging his passion for restoring and racing cars.
Peter Wolf, the band's lead singer, said he was "thinking of all the times we kicked it high and rocked down the house" in a tribute on Twitter.
Musician Nils Lofgren also paid tribute, saying he and his former band Grin had "learned so much" while opening for Geils's band in the early 1970s.
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John Geils Jr, the US guitarist who founded The J Geils Band and had a global hit with the song Centrefold, has died at the age of 71.