Jack Shepherd vanished while on bail over the manslaughter of 24-year-old Charlotte Brown, who died when Shepherd's speedboat hit a log and flipped on the River Thames in London in December 2015. The pair, who met on a dating website, had spent the evening at a restaurant before taking to the river.
The 31-year-old web designer was tried in his absence and sentenced in July to a six-year-prison term for gross negligence manslaughter. Georgia's Interior Ministry said in a statement that Shepherd had arrived at a police station with lawyers and turned himself in.
Television footage showed a bearded man entering the station, telling reporters: "Yes my name is Jack Shepherd, I was involved in a tragic accident." London's Metropolitan Police said it had been informed that Shepherd was in custody in the Black Sea nation. It said "extradition proceedings will begin immediately" once his identity was confirmed.
The victim's family and politicians including Prime Minister Theresa May had called on Shepherd to hand himself in. The news came a day after the victim's father, Graham Brown, met Britain's interior minister and vowed that "there can be no hiding place for Jack Shepherd."
Graham Brown wrote Wednesday on Facebook: "Just been informed that Jack Shepherd has been arrested in Georgia. Justice for Charlotte is close!"
Sophiko Megrelidze in Tbilisi, Georgia, contributed to this story.