We have used molecular-beam epitaxy to grow high-quality pseudomorphic Ni and Co1Ni9 films on Cu(001). From temperature-dependent surface magneto-optic Kerr effect measurements of these films, we have determined the finite-size scaling behavior of the Curie temperature of ultrathin films for a thickness range of n=2.5-16 monolayers (ML). The film thickness dependent Curie temperature for each of these ferromagnetic thin-film systems, T(C)(n), is described by a finite-size scaling formula: [T(C)(infinity) - Tc(n)]/T(C)(n) = [(n - n')/n0]-1/nu, where T(C)(infinity) is the bulk Curie temperature, n0 = 2.5 +/- 0. 5 ML for Co films and 3.5 +/- 0.4 ML for Ni and Co1Ni9 films is the microscopic length scale, and v=0.76 +/- 0.08 is the bulk correlation length exponent. An interesting result is that Tc(n) extrapolates to zero in the single mononolayer limit, n' = 1.