The newspaper said a new independent KC -- a senior barrister -- reviewed all of the evidence from the initial investigation which cleared Horner on the eve of the Formula One season.
The woman's complaint plunged the 50-year-old's future as head of one of the most successful teams in Formula One history into serious doubt.
But having always categorically denied the allegations, which emerged in February, and then being cleared, Horner has carried on in post and remained a familiar figure on this season's Grand Prix circuit.
A statement given to The Times by Red Bull published Thursday said: "Earlier this year a complaint raised against Christian Horner was investigated.
"That complaint was dealt with through the company's grievance procedure by the appointment of an independent KC who dismissed the grievance.
"The complainant exercised the right to appeal, and the appeal was carried out by another independent KC.
"All stages of the appeal process have now been concluded, with the final outcome that the appeal is not upheld.
"The KC's conclusions have been accepted and adopted by Red Bull. The internal process has concluded."
The female employee concerned has been suspended on full pay since March.
No sooner had Horner been cleared by Red Bull, he attended the season-opening Bahrain Grand Prix with his wife, former member of the Spice Girls pop group Geri Halliwell.
His position came under renewed scrutiny when the day after the verdict an anonymous email containing private messages allegedly between Horner and the female staff member was leaked to F1 officials and journalists.
