The 34-year-old former Juventus forward, who was born in France to Argentine parents, underwent medical tests in Buenos Aires on Friday prior to finalizing the deal.
River was relegated to the second division for the first time in its history last season.
Trezeguet says he wants ''to form part of the history of this club'' and is focused on getting River back into the top flight.
Trezeguet spent his childhood in Argentina and came through the ranks at Platense.
After leaving Spanish club Hercules in the summer, Trezeguet has been playing in the United Arab Emirates with Baniyas.