Baumgartner was the first Hungarian to compete in F1

The contract was finalised on Tuesday after the Hungarian government agreed to pay $4m (£2.5m) sponsorship to help finance the deal.

The 22-year-old made his Formula One debut for Jordan last season as a late replacement for Ralph Firman.

"Christmas has definitely come early for me this year," Baumgartner said. "This season's races have made me more determined than ever."

He added: "I have now realised my dream, although I don't think the reality of it has quite sunk in yet.

"I just want to start working with the Minardi team as soon as possible, so that I can be well prepared for the beginning of the season.

"It is a huge challenge, but I am really looking forward to it."

Baumgartner, the first Hungarian driver in F1, will replace Dutchman Jos Verstappen and his deal almost certainly means Briton Justin Wilson has no chance of continuing in 2004.

BAUMGARTNER FACTFILE 1994: Runner-up in Hungary's go-kart juniors 1997: Second in German Formula Renault. 1999: Third in European Formula Renault 2000: Competed in German Formula Three 2001: Competed in Formula 3000 2003: Test drives for Jordan; makes F1 debut for Jordan

Minardi owner Paul Stoddart said: "His performance last year - when he replaced Firman with very little notice - impressed me greatly.

"We're all impatient to start the 2004 season with Zsolt."

Baumgartner's team-mate will be Italian rookie Gianmaria Bruni.

Jordan are now Verstappen's only hope of staying in F1 as no other team has a vacancy.