The 49-year-old was found to have subjected a girl and a boy to multiple incidents of abuse, with the girl targeted between 1993-1996 and the boy between 2006-2010.
A five-day trial heard that Dott exposed himself in front of both children, touched them inappropriately and kissed them.
He was found guilty of two counts of lewd, indecent and libidinous behaviour.
Dott will be sentenced at a separate hearing in Edinburgh on September 29.
The World Professional Billiards and Snooker Association suspended Dott when the court charges were announced in April 2025.
Dott won the 2006 World Snooker Championship and was runner-up in 2004 and 2010.