  The complete expression of the heavy quark-antiquark potential up to order
$1/m^2$ is known from QCD in terms of Wilson loop expectation values. We use
that expression and a mapping, assumed to be valid at large distances, between
Wilson loop expectation values and correlators evaluated in the effective
string theory, to compute the potential. We obtain previously unknown results
for the spin and momentum-independent parts of the potential. These are
linearly rising with the distance and may be interpreted as relativistic
corrections to the string tension. We confirm known results for the other parts
of the potential. Finally, we compute the discrete spectrum of a heavy
quark-antiquark pair whose interaction is just given by the obtained potential.
