Helicopter pilot Babis Anagnostopoulos had initially claimed his 20-year-old wife died after violent burglars broke into their home on the outskirts of Athens last month as their young daughter slept.
He had said the men stole cash before escaping.
But his lawyers said that Mr Anagnostopoulos, 33, had now confessed to the crime, adding that he had expressed remorse for his actions. He had been arrested by police on Thursday evening.
Police investigators said analysis of data from a smartwatch worn by the victim had helped reveal inconsistencies in the pilot’s account of events.
An examination of the watch, mobile devices used by Crouch, and cameras, had established a timeline that contradicted the pilot’s testimony.
“Everything was staged for the crime scene to look like the scene of a robbery,” Costas Hassiotis, director of the greater Athens homicide division told reporters, adding that the suspect had tied his own hands and those of his dead wife.
In parts of his confession leaked to Greek media on Friday, the defendant claimed his wife had “kicked me out of bed” the night of the murder following a row.
“That night, of the 11th of May, we had another fight,” Anagnostopoulos admitted to the interrogators, according to reports. “She kicked me out of bed, and I saw her putting the baby back in the crib as I was leaving.”
Their daughter was unharmed, but the family dog was found choked to death, authorities said.
The story has shocked Greece and has made headlines worldwide. It prompted government officials to announce a €300,000 (£257,000) reward for information about the crime.
Mr Anagnostopoulos was detained after authorities summoned him for questioning on Thursday while he was attending a memorial service for Ms Crouch on the Aegean Sea island of Alonissos, where she grew up.
He was flown to Athens by helicopter from the nearby island of Skiathos, and interviewed for more than six hours before police announced that he was a suspect.
In a 16 May post on Instagram, Anagnostopoulos uploaded an undated photograph of the couple on a trip to Portugal for a wedding photoshoot, writing: “Always together. Farewell, my love.”
Greek police released a statement that read: “The investigation of the homicide of a 20-year-old native that took place on May 11, 2021 in Glyka Nera is now closed. The perpetrator is her 33-year-old husband, who confessed to his act.”