The homes will consist of three one-bedroomed flats, nine two-bedroomed flats, three two-bedroomed houses and 11 three-bedroomed houses.
Under Herefordshire Council's Unitary Development Plan, there is a requirement for nine of the planned homes to be affordable.
Leominster Town Council and Leominster Civic Society supported the scheme.
A letter was received from a nearby resident expressing concerns about the scheme leading to vandalism and anti-social behaviour.