James Bryson was found guilty of attacks on four youngsters between December 1969 and November 1994.
The now 69 year-old initially preyed on a girl at a flat in the north of Glasgow.
Bryson, of Clydebank, West Dunbartonshire, went on to rape the same child.
Bryson further indecently assaulted a young boy at another flat in the city.
He molested a second girl and then abused a third causing her to play a sick game which involved her taking off her clothes.
Bryson was convicted of a total of five charges following a trial at the High Court in Glasgow.
These included rape as well as using lewd and libidinous behaviour.
Judge Matthew Jackson KC deferred sentencing until April 14 in Edinburgh.
