Be assured; be certain.
Used other than figuratively or idiomatically: see believe, me.
Source: en.wiktionary.orgIt may be imitative of the Harvard anthem "Fair Harvard," which is also sung to the tune of "Believe Me, if All Those Endearing Young Charms." Source: Internet
The best known of Kern's songs from this period is probably " They Didn't Believe Me ", which was a hit in the New York version of the Paul Rubens and Sidney Jones musical, The Girl from Utah (1914), for which Kern wrote five songs. Source: Internet