The paper presents the approach to complex training of managers and faculty staff for system modernisation of Russian engineering education. As a methodological basis of design and implementation of the faculty development programme, the CDIO (Conceive-Design-Implement-Operate) Approach was chosen due to compliance of its concept to the purposes and tasks of engineering education development in Russia. The authors describe the structure, the content and implementation technology of the programme designed by Tomsk Polytechnic University and Skolkovo Institute of Science and Technology with the assistance of Chalmers University of Technology and KTH Royal Institute of Technology and other members of the CDIO Initiative. The programme evaluation based on the questionnaire results showed that the programme content is relevant, has high practical value and high level of novelty for all categories of participants. Therefore, the CDIO approach was recommended for implementation to improve various elements of the engineering programme such as learning outcomes, content and structure, teaching, learning and assessment methods. Besides, the feedback results obtained through programme participants' survey contribute to identification of problems preventing development of engineering education in Russia and thus serve as milestones for further development of the programme.