IIn situR magnetic resonance measurements of ultrathin Ni(111) on W(110) prepared in ultrahigh vacuum have been carried out to determine the thickness dependence of the critical exponent \ensuremath{\beta} and the Curie temperature ${\mathit{T}}_{\mathit{c}}$. We find that \ensuremath{\beta} changes drastically from 0.30 to 0.13 between 7 and 5 monolayers. We attribute this behavior to a crossover from a three- to a two-dimensional magnetic behavior. The observed ${\mathit{T}}_{\mathit{c}}$'s and linewidths also exhibit the effect of the dimensional crossover. Ni films \ensuremath{\le}4 layers thick show a truly two-dimensional magnetic phase transition with \ensuremath{\beta}=0.13.