The body of Marco Rallo, 50, was found in the city of Medellin on Saturday morning, Colombian daily El Tiempo reported.
The businessman from Rome had been beaten and was tied up when found, dressed in his pyjamas.
His wife María Clara Uribe Zárate was discovered two hours earlier, at around 4.20am, three kilometres away from her husband’s body.
The 37-year-old had also been beaten and was found with her wrists and ankles tied. Uribe Zárate’s body had been left next to an empty building and, like her husband, she was dressed in nightwear.
The couple are thought to have been killed by hanging, El Tiempo said.
Italy's foreign ministry said on Thursday an Italian had died in Colombia, but would not confirm the person's identity.
They are believed to be the victims of a violent robbery on Friday night, when a gang broke into their home to steal 500 million pesos (€189,000) from a safe.
The presumed gang leader, Gustavo Adolfo Vélez Arango, was arrested yesterday on murder charges. There are at least five other gang members who have not yet been caught, the newspaper said.
Medellin was the murder capital of the world in 1991, when there were 381 homicides per 100,000 inhabitants. The city was at the time lorded over by Pablo Escobar, the cocaine kingpin who was killed in 1993.
Vast security improvements since his death have seen the murder rate drop to around 80 per 100,000, according to figures from the Inter-American Development Bank (IDB).