Red Bull will take control of Minardi on November 1 with plans to use it as a junior team to groom drivers in its young driver scheme.
Australian aviation millionaire Stoddart hailed the agreement as "good news for Minardi" and insisted the team's base in Faenza, Italy would remain.
He added that he had received 41 approaches for Minardi since he took over the team in 2001.
The soft drinks company, which already owns Red Bull Racing, bought the Jaguar team from Ford last November.
It means Red Bull will run two Formula One teams from the start of the 2006 season onwards.
F1's secretive commercial agreement - that runs to the end of 2007 - is said to have measures to deter ownership of more than one team.
