Haci Ibramahain Koc, 53, was caught following a cold case review by the Met's Sexual Offences, Exploitation and Child Abuse Command.
The breakthrough came when detectives made a DNA match with Koc, who had provided a smaple for an unrelated matter in February.
Koc, now living in Devon, attacked the 28-year-old woman when she got into his cab on May 17 1994, at 2.30am.
During the journey, he stopped the car and dropped the passenger seat backwards.
He then pulled out a knife, held it to her face and cut off a lock of her hair before forcing himself on her.
The terrified woman was eventually able to get out of the car and flee for safety.
Yesterday, at Isleworth Crown Court, Koc was finally convicted of rape and jailed for 14 years.
Detective Inspector Keith Braithwaite, of the Serious and Complex Case Team, said: "Despite the overwhelming forensic evidence against Koc, he still denied the charge against him and
went to trial putting his victim in the witness box forcing her to relive her ordeal 20 years on.
"Koc has shown little if any remorse for this horrific crime. I hope the verdict and sentence gives some closure to the victim and would like to thank her for her courage and dignity throughout."
Uk standard www.standard.co.uk