The TOTEM collaboration has measured the proton-proton total cross section at √s=8 TeV using a luminosity-independent method. In LHC fills with dedicated beam optics, the Roman pots have been inserted very close to the beam allowing the detection of ~90% of the nuclear elastic scattering events. Simultaneously the inelastic scattering rate has been measured by the T1 and T2 telescopes. By applying the optical theorem, the total proton-proton cross section of (101.7±2.9) mb has been determined, well in agreement with the extrapolation from lower energies. This method also allows one to derive the luminosity-independent elastic and inelastic cross sections: σ(el)=(27.1±1.4) mb; σ(inel)=(74.7±1.7) mb.