Customers will also get a modem that will allow them to access the service, which will offer downloads with speeds of up to 8 Mb.
Vodafone will also provide a free technical helpline. However, the offer does not include a mobile handset.
In September, the group said it had agreed a deal with BT that would allow it to enter the broadband market without having to invest in a fixed line network of its own.
Stiff competition
A number of other mobile operators, including French-owned Orange, have begun offering bundled packages of services to their customers.
Carphone Warehouse and BSkyB, meanwhile, have announced cut-price broadband packages.
But surviving in this marketplace is a challenge, analysts said.
Stiff competition in the sector prompted the UK's second-largest telecoms group, Cable & Wireless, to leave the retail broadband market recently.
And on Thursday BT said increased competition meant that its share of new broadband customers fell to 25% from 30% in the three months to the end of September.