Charalambos Anagnostopoulos, 32, was asleep alongside his wife Caroline Crouch, 20, and their daughter when three burglars broke into their home in an affluent Athens suburb shortly before dawn on Tuesday.
The civil aviation pilot spoke of the “nightmare” ordeal of being tied to a chair while his wife was tortured at the family’s suburban home in Glyka Nera.
Ms Crouch, a student who was born in Greece but held a British passport, was tied up and strangled while her husband was bound and gagged. The baby was unharmed.
In an emotional tribute to his wife, Mr Anagnostopoulos told the Evening Standard: “She was the kind of person you want to spend the rest of your life with.”
The hooded intruders raided the property for cash and jewellery and killed their dog which was discovered hanging on the garden fence, police said.
Speaking to broadcasters outside what appeared to be their home, Mr Anagnostopoulos said: “I wish no-one ever goes through what we went through last night. It was a nightmare.
“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.”
The burglars escaped with cash and jewellery while Mr Anagnostopoulos called police after managing to loosen his bonds.
A rare £260,000 reward for information has been announced by the Greek Government.
The young couple were active on social media where Ms Crouch described herself as a digital creator and her husband referred to himself as a helicopter pilot and flight instructor.
Recent posts suggest the couple wed in May 2018. Last year, Mr Anagnostopoulos announced the birth of their baby daughter as the “best day in a man’s life.”
Ms Crouch is seen holding a baby, dressed in a teddybear onesie, during a day at the beach in January.
Alongside a photograph of the couple shared in July last year, her husband wrote: “Happy Birthday to my awesome wife, closest friend, and best mom our daughter could have.”
The minister responsible for public order, Michalis Chrisochoidis, described the killing as “particularly heinous”.
He added: “One rarely encounters such barbarity in Greece, in Greek society, even among criminals.”
Two teams of detectives have been set up to handle the investigation, he said.