Adhesion of biological cells is essential for various processes, including tissue formation, immune responses, and signaling. It involves multiple length scales, ranging from nanometers to micrometers, which are characteristic of (a) the intercellular receptor-ligand binding that mediates the cell adhesion, (b) the spatial distribution of the receptor and ligand proteins in the membranes of adhering cells, (c) adhesion-induced deformations and thermal undulations of the membranes, (d) the overall size of the interface between adhering cells. Therefore, computer simulations of cell membrane adhesion require multiscale modeling and suitable approximations that capture the essential physics of the system under study. Here, we introduce such a multiscale approach to study membrane adhesion mediated by the CD47-SIRPα binding, which is an immunologically relevant process. The synergetic use of coarse-grained molecular dynamics simulations and mesoscale kinetic Monte Carlo simulations allows us to explore both equilibrium properties and dynamical behavior of adhering membranes on the relevant length scales between 1 nm and 1 μm on time scales ranging from 0.1 ns all the way up to about 20 s. The multiscale simulations not only reproduce available experimental data but also give quantitative predictions on binding-induced conformational changes of SIRPα and membrane-mediated cooperativity of the CD47-SIRPα binding as well as fluctuation-induced interactions between the CD47-SIRPα complexes. Our approach is applicable to various membrane proteins and provides invaluable data for comparison with experimental findings.