Most likely related to Hebrew כֶּלֶב (kelev) meaning "dog". An alternate theory connects it to Hebrew כָּל (kal) meaning "whole, all of" and לֵב (lev) meaning "heart". In the Old Testament this is the name of one of the twelve spies sent by Moses into Canaan. Of the Israelites who left Egypt with Moses, Caleb and Joshua were the only ones who lived to see the Promised Land.
As an English name, Caleb came into use after the Protestant Reformation. It was common among the Puritans, who introduced it to America in the 17th century.