Born in Montevideo, Canobbio began his career with C.A. Progreso in 1997. In three seasons there, he was impressive enough to be signed by country giants C.A. Peñarol in 2001, where he spent two campaigns scoring more than 30 official goals while helping the capital side to the 2003 league title. In late July 2003, Canobbio was acquired by Rafael Benítez's Valencia CF, where he was played mainly as a substitute. Benítez hadn't asked for his signing, and he famously commented that he had been waiting for a sofa and he had been brought a lamp instead. Having scored just once throughout the season, in a 2–2 home draw to RC Celta de Vigo, he nonetheless managed to make ten appearances in the team's 2004 UEFA Cup conquest, netting once in the 3–2 success against Beşiktaş JK.