Andrea Leadsom said she was "delighted" with the agreement, which came after rescue talks over the weekend.
She tweeted: "Delighted that we have reached agreement with Flybe's shareholders to keep the company operating, ensuring that U.K. regions remain connected. This will be welcome news for Flybe's staff, customers and creditors and we will continue the hard work to ensure a sustainable future."
Transport Secretary Grant Shapps also welcomed the agreement.
He said: "Delighted we've been able to work closely with Flybe to ensure Europe's largest regional airline is able to continue connecting communities across Britain. @transportgovuk will undertake an urgent review into how we can level up the country by strengthening regional connectivity."
Chancellor Sajid Javid had held talks with the business and transport secretaries to discuss if the loss-making regional carrier can defer paying this year's estimated air passenger duty (APD) bill of £106 million for three years or whether the tax should be cut for all domestic flights, according to multiple reports.
Airlines claim APD restricts connectivity and passenger growth.
Passengers on domestic flights pay £26 in APD for a return trip, with higher rates for longer flights and premium cabins.
The tax is expected to be worth £3.7 billion to the Treasury in 2019/20.
The deal means Flybe has avoided being the second UK airline to fail in four months, after Thomas Cook went bust in September.