"Welcome, King David. I give you the shirt that will allow you to communicate with the public from today," said club president Guillermo Lorente.
Trezeguet, who is of Argentinian descent, recently left River Plate, the club he supported as a boy and signed for in 2012.
"I'll be a team that everyone admires and has won the Argentine title,” he said. “I'm fit and my goal is to win the [Inicial] tournament and the Copa Libertadores.
"This is a very special day. Newell's were interested in me for a month when River told me to leave, and it was the only real and serious proposal.
"I feel very well and ready to play again."
Trezeguet has been out of action with a knee injury since March 30. Newell’s Old Boys said they had put him through an exhaustive medical examination.