Taking advantage of both the high mass resolution of the COSY-11 detector and the high energy resolution of the low-emittance proton beam of the cooler synchrotron COSY, we determine the excitation function for the pp→ppη(') reaction close to threshold. Combining these data with previous results, we extract the scattering length for the η(')-proton potential in free space to be Re(a(pη(')))=0±0.43 fm and Im(a(pη(')))=0.37(-0.16)(+0.40) fm.