Astori was of Italian (Lombardy-Piedmont) descent; both grandparents of his paternal and maternal side were from the towns of Como and Novi Ligure.

After graduating, he began working with the then deputy minister of livestock and leader of the National Party, Wilson Ferreira Aldunate.

[8] In 2005, with the inauguration of Tabaré Vázquez, the first president of the Broad Front, Astori was appointed Minister of Economy and Finance.

The presidential candidate of the Broad Front Daniel Martínez proposed him as Minister of Foreign Relations in a possible government.

He was a supporter of trade pacts with the United States, the European Union, the People's Republic of China and India, with the Chilean "open regionalism" as a model.