Norman Pender, 65, repeatedly sexually abused two females between April 1986 and October 1997.
The High Court in Edinburgh heard how Pender, who was capped four times for Scotland in the late 1970s, preyed on the women at various addresses in Hawick, Roxburghshire.
The victims cannot be identified for legal reasons, but one of them told the court the abuse started when she was eight and continued until she was 19.
Pender started abusing his second victim in January 1996 when she was nine.
The former used car salesman continued to abuse her until she was 11.
A jury of nine women and six men returned verdicts of guilty to three charges of using lewd and libidinous behaviour towards the women.
They also returned a verdict of guilty on one charge of sexual assault after spending two days deliberating their verdicts.
They gave a verdict of not proven to an allegation that he repeatedly raped his first victim.
The court heard Pender was a first offender. Defence solicitor advocate Iain Paterson asked judge Lord Stewart to continue his client's bail because Pender wanted to spend time with his sick wife and his mother, who is in her 90s.
But Lord Stewart refused and remanded Pender in custody, saying it would not be in the interests of justice for him to remain at liberty.
He deferred sentence to the High Court in Paisley on January 15 next year for reports but warned that jail time would be a "probable" outcome.
Pender then thanked the judge and headed to the cells. One of his daughters then shouted: "Love you dad."
Pender, of Cavers, Hawick, who had played rugby for his home town club, also served as a Liberal Democrats' councillor on Scottish Borders Council between 1998 and 2003.
He was also the chairman of the Hawick Lady Riders Association, an organisation set up to campaign for women in the town to ride horses in the community's Common Riding Festival. Females were not allowed to ride in the festival between 1932 and 2000.
On the first day of the trial, Pender's first victim told prosecution lawyer Alison Di Rollo what the retired sportsman did to her.
The woman, who gave her evidence behind a screen, took a deep breath as she described how she was repeatedly sexually assaulted.
When Ms Di Rollo, the head of the Crown Office's national sex crimes prosecution unit, asked her whether she gave her consent to these acts taking place, the woman replied: "No."
The advocate depute asked how she felt after the abuse took place. The victim replied: "Dirty, sick, lonely, ashamed."
When Ms Di Rollo asked her how many times the sex attacks took place, she replied: "Far too many times to count."
The woman told the court she told a boyfriend about the abuse when she was in her late teens.
However, she did not contact the police until many years later.