However, it is believed police there were only contacted with the information last week.
In the television interview, Shepherd smiled as he explained how the crash was a “tragic accident”.
Asked why he chose to flee to Georgia, he explained “there’s a lot going for Georgia.” A lawyer representing him later said said he has friends in the country.
His decision to hand himself in followed a renewed appeal by Miss Brown’s parents, Graham Brown and Roz Wickens, and her two sisters.
On Tuesday the family met Sajid Javid, the Home Secretary, before Mr Brown appeared on television appealing for his daughter’s killer to “do the right thing”.
Last night, Mr Brown, a 55-year-old prison manager from South East London, told The Telegraph he felt “an overwhelming sense of relief”.
“I cried when I heard,” he said. “It doesn’t bring Charli back, but it’s a great release and an overwhelming sense of relief.
“It’s been such a journey that the fact he’s now in custody means we can deal with our lives better and move on without this terrible distraction.”
However, Miss Brown’s sister, Katie, condemned Shepherd for appearing “smug” in the interview, adding: “I don’t understand how someone can go on the run for two crime and be found guilty and then just walk straight in with a very smug look on his face and claim innocence.”