The wetting of planar solid surfaces of Rb by superfluid ⁴He films at T = 0 K is examined theoretically the calculations were carried out by (i) using the most elaborated nonlocal density functional known as the Orsay-Trento proposal and (ii) assuming that the helium atoms interact with the substrate via the potential recently worked out by Chizmeshya, Cole, and Zaremba. The asymptotic surface tension was evaluated by applying two different procedures. Our results indicate that films of ⁴He wet Rb at zero absolute temperature.