We report the final result of the CUORICINO experiment. Operated between 2003 and 2008, with a total exposure of 19.75 kg y of 130Te, CUORICINO was able to set a lower bound on the 130Te 0nDBD half-life of 2.8 10^{24} years at 90% C.L. The limit here reported includes the effects of systematic uncertainties that are examined in detail in the paper. The corresponding upper bound on the neutrino Majorana mass is in the range 300--710 meV, depending on the adopted nuclear matrix element evaluation.