Context : The Gaia-ESO Public Spectroscopic Survey is obtaining high-quality spectroscopic data for about 10 ^ { 5 } stars using FLAMES at the VLT . With the FLAMES-UVES link , high-resolution spectra are being collected for about 5 000 FGK-type stars . Aims : These UVES spectra are analyzed in parallel by several state-of-the-art methodologies . Our aim is to present how these analyses were implemented , to discuss their results , and to describe how a final recommended parameter scale is defined . We also discuss the precision ( method-to-method dispersion ) and accuracy ( biases with respect to the reference values ) of the final parameters . These results are part of the Gaia-ESO second internal release and will be part of its first public release of advanced data products . Methods : The final parameter scale is tied to the one defined by the Gaia benchmark stars , a set of stars with fundamental atmospheric parameters . In addition , a set of open and globular clusters is used to evaluate the physical soundness of the results . Each of the implemented methodologies is judged against the benchmark stars to define weights in three different regions of the parameter space . The final recommended results are the weighted-medians of those from the individual methods . Results : The recommended results successfully reproduce the benchmark stars atmospheric parameters and the expected T _ { eff } - \log~ { } g relation of the calibrating clusters . Atmospheric parameters and abundances have been determined for 1301 FGK-type stars observed with UVES . The median of the method-to-method dispersion of the atmospheric parameters is 55 K for T _ { eff } , 0.13 dex for \log~ { } g , and 0.07 dex for [ Fe/H ] . Systematic biases are estimated to be between 50-100 K for T _ { eff } , 0.10-0.25 dex for \log~ { } g , and 0.05-0.10 dex for [ Fe/H ] . Abundances for 24 elements were derived : C , N , O , Na , Mg , Al , Si , Ca , Sc , Ti , V , Cr , Mn , Fe , Co , Ni , Cu , Zn , Y , Zr , Mo , Ba , Nd , and Eu . The typical method-to-method dispersion of the abundances varies between 0.10 and 0.20 dex . Conclusions : The Gaia-ESO sample of high-resolution spectra of FGK-type stars will be among the largest of its kind analyzed in a homogeneous way . The extensive list of elemental abundances derived in these stars will enable significant advances in the areas of stellar evolution and Milky-Way formation and evolution .