He went on the run pending his Old Bailey trial over the death of 24-year-old Charlotte Brown. Shepherd was convicted in his absence in July last year.
Georgia’s embassy in London said he surrendered himself to police today after her family increased their calls for him to return to face justice.
Her father Graham Brown celebrated the “overwhelming” development, writing on Facebook: “Justice for Charlotte is close!”
A heavily-bearded Shepherd was seen smiling as he entered a police station in Georgia’s capital Tbilisi.
Then, he told reporters: “I was in a tragic accident.”
Ms Brown, from Clacton-on-Sea in Essex, died in December 2015 when 31-year-old Shepherd’s boat flipped into the wintry waters of the River Thames in London.
The pair had been on a Champagne-fuelled first date.
Shepherd, originally from Exeter, was sentenced in his absence to six years in prison for manslaughter by gross negligence.
A spokesman for the Georgian embassy said: “He has just surrendered himself to the Georgian Police and now the police undertakes relevant detaining formalities.”
The family of Ms Brown, known to loved ones as Charli, ramped up pressure in recent weeks and met with Home Secretary Sajid Javid on Tuesday and renewed calls for Shepherd to surrender himself.
A day later Shepherd, wearing a long coat, jeans and a checked scarf, waved and smiled as he walked into the station from a black car.
Speaking to journalists, he said: “Yes, my name is Jack Shepherd, I was involved in a tragic accident ... in which a lady called Charlotte Brown tragically died.”
Georgia’s internal ministry said the web designer surrendered himself alongside lawyers.
Ms Brown’s father told BBC Radio 5 Live he felt “an overwhelming sense of emotion” at the news.
“My opinions towards Jack Shepherd is that he’s a very crass, reckless man, who managed to abscond and stick two fingers up at the judiciary,” Mr Brown said.
“He’s got to come back to atone for all that and I think that he’s done the right thing and thank goodness he’s realised that now and handed himself in.”
Charlotte’s sister Katie Brown voiced surprise over Shepherd’s “smug” appearance on clips aired by a Georgian TV channel.
She told BBC News: “I feel very surprised at how smug he looks to be honest.
“It just shows a very arrogant man.
“I don’t understand how someone can go on the run for two crimes and be found guilty and still then just walk straight in with a very smug look on his face and claim innocence. It’s unbelievable.”
She said she found his claims of innocence “baffling”, adding: “The thing that I find quite baffling is he’s still maintaining his innocence.
“Someone who’s run away from this doesn’t scream an innocent man’s actions to me. Why did he run away if he’s claiming innocence?”
Mr Javid, who a day earlier warned “there can be no hiding place” for Shepherd, celebrated his arrest.
“We will seek to swiftly extradite him to Britain,” he said. “It is vital Charlotte Brown’s family see justice done.”
The family’s MP, James Brokenshire, said Shepherd’s “wanton and selfish actions” had heaped further strain on the family “at a time of unimaginable grief”.
“Nothing can take away their loss, but I hope this may now offer some sense of justice,” the communities secretary said.
Scotland Yard, the force leading the investigation, said officers had been updated by the National Crime Agency on the development and are awaiting confirmation of his identity.
But, the Metropolitan Police added that once identity was secured extradition proceedings “will begin immediately” against Shepherd, who was wanted on an international arrest warrant.
Georgian law states that extradition is granted over convicted individuals if they have been sentenced to at least four months’ imprisonment.
While Shepherd was on the run from the law, his lawyers have been working to appeal against the conviction.
Solicitor Richard Egan: “In the light of today’s developments I don’t think it would be appropriate to comment further until Mr Shepherd is back in the jurisdiction.”