Gillian Kay, 44, survived the head-on collision caused by John Gribben, but friend Joan Price, 59, was killed in the incident.
The pair were returning from brass band practice when tragedy struck on January 30, 2017.
Jurors heard how one motorist described their behaviour as “absolute madness”.
Knox eventually lost control of his powerful Volkswagen Golf GTI and ploughed head on into Price’s Nissan Pulsar.
The support worker died instantly while her passenger, Ms Kay, was left badly hurt in the collision and now suffers from mobility issues.
Prosecutors claimed Knox and Gribben fled the carnage in the latter’s private-registration Audi A3.
Despite the death, Gribben took part in further high speed driving just two months later and was described as using “Ayrshire roads as a racetrack”.
Gribben, then 19, was found guilty of causing death by dangerous driving.
Knox, then 20, was jailed for five years and four months after he pled guilty to the same charge.
Following an out-of-court settlement, Ms Kay said: “The last few years have been truly life-changing for me and my family – there were times when I thought there was no real recovery in sight.
“My physical injuries may have improved, but they will not go away and will affect me for the rest of my life – and above that there’s the loss of a dear friend whom I’ll never forget.
“I am grateful to everyone who has supported me during this time, but as both the criminal and civil cases are over I would now like my privacy respected.”
The exact amount of the six-figure settlement has not been disclosed.
Damian White, partner at Digby Brown in Ayr, said: “Gillian sustained very serious injuries as a result of a completely avoidable road traffic accident that will affect her for the rest of her life.
“I have great respect for the strength and dignity she has maintained since the incident and I wish her all the best for the future.”