The 27-year-old from Norwich was formally unveiled on Tuesday as the new team-mate of Giancarlo Fisichella.
He has signed a three-year deal and will become the fourth Briton on the F1 grid.
Firman will line up alongside David Coulthard, Jenson Button and fellow rookie Justin Wilson in the season-opening Australian Grand Prix on 9 March.
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I'm impressed with his very cool and disciplined approach
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Team boss Eddie Jordan
"I am thrilled to have this chance to race in Formula One," said Firman. "I still can't believe it - it has not really sunk in yet."
"This is what I have always dreamed of and I have never given up hope of getting into F1.
"That first race is going to be special, but there is a lot of work to do yet.
"But with the new points system, with points going down to the top eight, hopefully I will have some good opportunities to score points."
Firman was set to defend the Formula Nippon title he won in Japan last year, with Brazil's Felipe Massa favourite to land the Jordan seat vacated by Japan's Takuma Sato.
Massa, though, appears to have been unable to have come up with the necessary £3m-plus sponsorship to bolster Eddie Jordan's budget.
'Awesome partnership'
Firman will hold his first test with the team next week in Valencia, Spain.
"I have worked hard to build up my experience whilst racing in Japan, so although F1 will be something new I feel ready and quite comfortable with it," he added.
"I am really looking forward to going to Melbourne next month."
Jordan team boss Eddie Jordan is also confident that Firman will make the transition to F1 with relative ease.
"He may be a rookie in F1 terms but Ralph brings a lot of racing experience and a formidable track record along with his enthusiasm and commitment," Jordan said.
"I'm impressed with his very cool and disciplined approach and I have a lot of confidence that he and Fisichella will be an awesome partnership on the track."