In this paper, the Bouc-Wen friction model parameters of two elastic rough interfaces are determined analytically based on multi-asperity contact theory. To this, the three main contact characteristics parameters of the rough interface, including slippage friction force, slippage displacement limit, and tangential interface stiffness, are determined. According to multi-asperity contact theory, these three main contact characteristics are physically meaningful parameters related to measurable rough surface parameters such as standard deviations of asperity heights, mean radius of asperity summits, and areal density of asperities. The new frictional contact model of the rough interface is produced as a first-order differential equation form. This model is obtained using exponential function curve-fitting on the interface stiffness behavior of the rough interface. Finally, the constant parameters of the Bouc-Wen friction model are related to three main contact characteristic parameters using a first-order differential equation. In other words, this paper proposed an analytical way to establish the Bouc-Wen model by measurable topography parameters of contacted rough surfaces. The capability and application of the proposed model in engineering problems are investigated and validated experimentally.