The Colombian was appointed in September after three years in charge of Mexico and coached his new team to a 1-1 draw with South Africa in November.
Media reports have said that he was unhappy in the South American nation and he confirmed his departure at a news conference in the Paraguayan capital.
"I am here to tell you that by mutual agreement with the APF (Paraguayan Football Association) and for my own family reasons, I unfortunately cannot continue as the Paraguay national coach," Osorio said.
"It was a family matter that I haven’t been able to resolve," he added.
"I leave here happy, very grateful. It was an enriching and extraordinary experience."
Osorio, a former coach of club sides in Colombia, Mexico, Brazil and the United States, replaced Francisco Arce, who left after failing to lead Paraguay to the 2018 World Cup finals in Russia. Paraguay also failed to qualify for the Brazil World Cup in 2014.
APF officials said they will seek a replacement immediately and they will hope to have someone in the dugout in time for the Copa America, which begins in Brazil in June.
The Paraguayans are drawn in Group B, along with Argentina, Colombia and Qatar.
They have two friendlies lined up in March, on the 22nd against Peru in New Jersey and four days later against Mexico in Santa Clara.
(Writing by Andrew Downie; Editing by Toby Chopra and Toby Davis)
