Doing business successfully in the 21st century is a real challenge. The accelerated business dynamics, the necessity of rapid adaptation to macroeconomic developments, and the increasing global competitiveness require companies to have excellent business performances. In order to achieve world-class performances and make the most of their internal competitiveness reserves, companies need a systematic approach to improvements and progress, and they apply a variety of methodologies for improvement. Lean methodology is the most popular methodology for improvements in the production sector, and a practical standard in the automotive industry. Its popularity is also growing in the service sector. Lean’s potential is large, but the level of successful lean implementation, that is the achievement of lean transformation of companies is not satisfactory. By examining lean principles and philosophy, obstacles and traps of lean implementation, and the lean transformation process, it was concluded that one of the fundamental supporting factors of lean transformation is strategic management which is very often neglected and thus one of the main reasons for failure. The work also examined and explained the particularities and influential elements of lean transformation and the corresponding strategic management process, in order to obtain a wide picture, a context, and an insight into the complexity of the problem itself. It was determined that a specific strategic management process complementary to lean is the hoshin kanri, which, such as lean, has its roots in the Japanese management. The hoshin kanri philosophy and the way of working are based on Deming's PDCA cycle, on which principle the strategic management process itself is implemented. It is characterised by the engagement of all employees at all stages of the strategic management process, from formulation to implementation and control, reaching consensus at all levels of the company, clarity of vision and personal roles in the realisation of the strategy, motivation and common goal. Based on the carried out theoretical research, conclusions, and practical examples considerations, a synthesis was deduced and the essence itself of the object of work was presented through a proposal (model) of a specific approach to strategic management process for companies’ lean transformation. The application of lean as improvements methodology is underrepresented and immature in Croatia, which offers great possibilities for the advancement of companies by selecting lean as their business strategy.