The group hopes to take advantage of its enormous branch network – at 11,500 the Post Office has more branches than all banks and building societies together.
It has more than 3m customers, an £18bn savings book and a mortgage book of £3bn.
The scheme will begin in 29 branches in East Anglia today before being rolled out to the rest of the country next year.
The standard account will offer a debit card, free in-credit banking services and a chequebook.
A new packaged account costs £8 per month, including travel insurance, travel booking services and identity theft protection.
And a control account costs £5 per month but has no charges on payments returned unpaid like direct debits and standing orders.