In this research work, the magnetic properties of laser welded Fe–Co–7.15 wt%V foils were investigated and a statistical analysis of Nd:YAG laser beam welding of these foils was done using response surface methodology (RSM). The results indicated that the welded samples experience a significant decrease in their magnetic properties. The input process parameters such as lamping current (130–160 A), pulse duration (1.5–3 ms), travel speed (50–200 mm/min) and focused position (2 to 0.5 mm) were selected suitably in order to obtain the desired output, i.e., the magnetic properties of the welded samples. This paper highlighted the use of RSM by designing a four-factor five-level central composite rotatable design matrix with the full replication for planning, conduction, execution and development of mathematical models. The main effect of each factor and the interaction effect with other factors were determined quantitatively and presented graphically. Analysis of variance and other adequacy measures were employed to check the adequacy of the developed model. A laser beam with lamping current, pulse duration, welding speed and focused position of 145 A, 1.5 ms, 125 mm/min and 0.5 mm respectively were identified as the optimal set of laser welding parameters to obtain a welded area with desirable magnetic properties.