The encounter between bubble pairs can be happened in the bubble flows and may result in coalescence, which is one of the most important elementary physical processes occurring in liquid columns. Sufficient knowledge of the coalescence process of two bubbles can lead to a better description of the bubbly flow’s behavior. Effects of uniform magnetic fields on the interactions and coalescence of dielectric bubbles were not studied up to now; therefore in this research, interactions and coalescence of two bubbles in a viscous stagnant liquid has been simulated numerically. Considered bubbles are spherical and fluids are stagnant, initially. Both liquid and gas phases considered being incompressible and dielectric where applied magnetic field is uniform. In the numerical simulation of the problem, the Finite Volume method was applied using the SIMPLE algorithm to discretizing the governing equations while the finite difference method was used for discretizing of the magnetic field equation. For simulating the interface of two phases, the level set method has been incorporated. The results outlined in the present study well agree with the existing experimental and numerical results. Obtained results show that applied uniform magnetic field affects shape, dynamics and also interactions and coalescence of bubble pairs. Applied magnetic field enhances coalescence between in-line rising bubbles. Therefore, the external uniform magnetic field could be used for contactless control of the coalescence process between bubbles.