"Trezeguet is already a new River Plate reinforcement, that's clear. He passed the medical revision and will sign this week," River said on the club's website.
River added that after signing Trezeguet, who was to have been unveiled on Monday evening, was going to fly "to the United Arab Emirates to sort out some issues he had left undone in the Asian country" where he played for Baniyas of Dubai.
"He will be present on River's first training day of the New Year at the Monumental stadium on January 4, when he will be formally presented to the media as a member of the squad and wear the team's colours of white with a red diagonal sash for the first time."
The Rouen-born 34-year-old, a River fan since his boyhood in Buenos Aires, is joining the club as a free agent but has issues to resolve concerning his contract with Baniyas whom he joined from relegated Hercules in Spain this year.
The former Juventus ace, who helped France win the World Cup in 1998 and the European championship in 2000, said last week it was a dream for him to play for River in Argentina.
He is expected to make his debut for River, record 33 times Argentine first division champions, in the Nacional B in February following the summer recess.