The 63-year-old, of Tamneyreagh Park in Eglinton, has been remanded in custody awaiting his sentencing on September 9.
The jury returned unanimous guilty verdicts on six indecent assault charges, and found McKeever not guilty of a seventh charge.
He was also convicted on two charges of gross indecency – one unanimously and the other by a majority of ten-to-two.
The offences happened on dates between August 1981 and December 1988.
When the allegations came to light, the SDLP suspended him from the party pending the outcome of the criminal justice process.
His victim, who wishes to remain anonymous, has released a statement today saying: “Nothing is going to erase what that man done to me but today justice has been served.
“If anybody has been in the same situation as me I would ask them to come forward to police and speak out.”
Detective Constable Ruth Phelan said: “This has been a very traumatic ordeal for the victim and I commend her for bravely coming forward to report to us.
“I hope that her strength and confidence in the Police to conduct a thorough investigation encourages other victims of child abuse who have felt silenced, to come forward too.
“We have a team of dedicated detectives who are determined to bring anyone involved in any form of child abuse before the courts to answer for their crimes, no matter when they occurred.
“I would continue to encourage anyone who has experienced any form of sexual abuse to contact police on 101, or in an emergency call 999.
“Once you’ve made a report, you don’t have to come into a police station, detectives can arrange to meet you at a time and place that best suits you.”