Berizzo replaces Juan Carlos Osorio, who resigned last week after an unhappy five months in which he led the landlocked South American nation in just one game.
"Negotiations have been completed with 49-year old Argentine national Eduardo Berizzo Magnolo to be the new coach," the APF said.
Berizzo, who was Jorge Sampaoli's assistant with Chile and enjoyed success at Chilean side O'Higgins, will reveal members of his backroom staff and be officially introduced to the media on Friday, it added.
Berizzo's first games in charge will be next month, when Paraguay play friendlies against Peru in New Jersey on the 22nd and Mexico in Santa Clara four days later.
His first competitive matches will come in the Copa America, which begins in Brazil in June.
The Paraguayans have been drawn in Group B, along with Argentina, Colombia and Qatar.
(Reporting by Andrew Downie; Editing by Christian Radnedge)
