The move is the latest in the industry and will apply to all its brands including its intermediary arm-Platform and Britannia from Monday 1 April.
The lender said that although the clause wording will remain part of some documentation and processes in the short term, while system updates are made, all changes will be implemented to remove the condition by 19 May.
“Landlords will be able to let to tenants at their discretion from 1 April 2019 and in line with the other conditions of let which are set out in the terms and conditions of their mortgage,” it said.
The announcement follows the high-profile campaign which built after Mortgage Solutions exclusively revealed the plight of landlord Helena McAleer.
It eventually resulted in McAleer’s lender NatWest overhauling its lending policies to allow letting to tenants on benefits.
Co-operative managing director of mortgages Gordon Soutar said: “We are glad to be able to remove this condition to the benefit or our landlords and prospective tenants who previously may have been restricted from taking up tenancy due to the inclusion of this letting condition in our mortgage terms and conditions.
“Our charity partner Centrepoint have raised this issue and the potential impact that this condition of let could have on the young people they work with.
“This is not a condition that we want to continue to include in the mortgages that we offer and we will no longer enforce these clauses in our mortgage terms and conditions from Monday 1 April and we will completely remove this condition from our processes and systems with a completion date of 19 May 2019.”