The contract, awarded by the Office of Government Commerce (OGC), is expected to save the Treasury £38m.
Treasury chief secretary Andrew Smith said any public sector body could share the savings negotiated by the OGC.
"This is the first in a series of streamline initiatives from the OGC and demonstrates the savings that can be achieved with a co-ordinated approach to procurement across government.
"The agreement makes available Vodafone's best value for the Government to the whole of the public sector, including local authorities and the NHS, on government contractual terms and without the need for local competitions," said Smith.
The deal is a "strategic partnership", not an exclusive contract, and 50,000 central government users have contracts with other telecoms companies.
BTCellnet, number two in the UK mobile market and boasting contracts with 55 of the FTSE's 100 companies, claimed the agreement would make little difference.
"It does not affect any relationship we have in the public sector," a BT spokesperson said. "We like to think we will remain competitive and offer a very good alternative."
Vodafone's preferred-supplier status means that any department choosing an alternative supplier must demonstrate it has got a deal better than Vodafone could offer.