The 86 year old stepped back from ministry in April amid "health concerns".
Written on his Facebook page, a statement from the family said: "It is with great sadness that we share this news that Norm Geisler passed away peacefully this morning.
"He has left behind an amazing legacy that will continue to have a ripple effect for many years to come."
Described as a cross between Thomas Aquinas and Billy Graham, Geisler authored over 100 books and taught theology, philosophy, and apologetics for over 50 years.
He also founded Southern Evangelical Seminary, one of the USA's most respected teaching colleges.
His funeral will take place in Charlotte, North Carolina at 3pm on Saturday 6th July.
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