250,000 benefit claimants who receive their money by cheque, cashed the Post Office, are affected.
The decision is a blow to the Post Office which had tendered for the contract.
It will take at least a year for the cheque payments to be phased out.
Nearly 250,000 receive cheques, often because they do not have an appropriate bank account for for direct electronic payment, out of 18 million benefit recipients.
Most of the cheque users are on in-work benefits such as jobseekers allowance or income support. But 60,000 are pensioners and 38,000 are on Disability Living Allowance.
The Department for Work and Pensions also announced a £73m fund to support credit unions, in an effort to provide alternatives to loan sharks.
Ministers expect the Post Office will link to credit unions to provide families with wider access to banking services.
The DWP said Post Office branches could also play a part in delivering the new Universal Credit, which is replacing several benefits. They could add to their current work verifying identities for National Insurance applications and pension claims.