An analysis has been presented to study the effects of viscous dissipation and Joule heating on two-dimensional steady stagnation-point flow of an incompressible viscous electrically conducting fluid over a stretching plate with Newtonian heating and convective boundary condition in the presence of uniform transverse magnetic field. Similarity variables reduce the governing boundary layer partial differential equations to a set of non-linear ordinary differential equations and solved numerically using the Galerkin finite element method. Effects of various parameters such as stretching parameter, magnetic parameter, conjugate parameter, Prandtl number and Eckert number for velocity and temperature distributions have been discussed in detail through graphical representation. Moreover, numerical results of local skin-friction coefficient and local Nusselt number for different values of controlling parameters have been shown in tabular form and analyzed. Numerical values have been validated by comparing the present results with previously published works.