The main works are scheduled to start in July with completion of the scheme in August 2015.
The Department for Transport has agreed to fund £9.6m of the £16m Leeds Rail Growth scheme.
The new stations will be at Apperley Bridge and Kirkstall Forge. The Apperley Bridge Station will include a park and ride site to serve both Leeds and Bradford while the Kirkstall Forge station will kick start a £400m mixed-use development at the Old Forge site. This development is set to include approximately 1,000 new homes and extensive commercial buildings.