The 33-year-old helicopter pilot and flight instructor Babis Anagnostopoulos had publicly claimed student Caroline Crouch, 20, had been killed during an invasion of the couple's home near Athens.
Ms Crouch, a British national who grew up in Greece, was found murdered in a bedroom on May 11 after her husband reported the crime to the police.
Anagnostopoulos made statements hours after the killing, telling reporters they had been tied up by robbers who broke into their home in Glyka Nera.
In a statement on Thursday, Greek police said: “Investigation of the homicide of a 20-year-old native that took place on May 11, 2021, in Glyka Nera.
“The perpetrator is her 33-year-old husband, who confessed to his act.”
He reportedly confessed after more than eight hours of interrogation, with Hellenic Police confirming he had “admitted to his actions”, reports the Mirror Online.
The couple's infant daughter was at home at the time of Ms Crouch's death but was not harmed. Police had issued a 300,000 Euro (£262,000) reward for information.
On Thursday, authorities said new evidence had come to light and that the husband had been summoned for questioning after attending a memorial service on the Aegean Sea island of Alonissos, where Ms Crouch grew up.
He was transported to Athens by helicopter from the nearby island of Skiathos.
The mayor of Alonissos, Petros Vafinis, told newsit.gr: “The police were very discreet and there was no disturbance at the memorial. I do not know if he has been called for identification or to give a new statement.”
He previously claimed his wife was strangled to death in front of her 11-month-old daughter Lydia after burglars raided their home.
Anagnostopolous told police that he was tied up and gagged.
He had previously described the murderer as tall, dark-skinned, overweight and under 30 years old.
When officers arrived at the couple’s home they found the couple’s 11-month-old daughter Lydia hitting her dead mother in an attempt to wake her up.
Mr Anagnostopoulos had told broadcasters at the time that the attack has been a “nightmare”.
“I wish no-one ever goes through what we went through last night. It was a nightmare,” he said.
“We begged the thieves not to harm us. We told them where the money was and asked them to leave us alone. The police will catch them.”
Additional reporting by the Associated Press.