Former Estoril boss Silva takes over from Leonardo Jardim, who stepped down on Tuesday amid rumours that he is to replace Claudio Ranieri at Ligue 1 side Monaco.
Silva took charge of Estoril in September 2011, leading them to promotion to the top flight in his maiden season in charge.
Estoril finished fifth in 2012-13, qualifying for the UEFA Europa League, and improved further this season as Silva guided them to fourth spot.
And the 36-year-old, who left Estoril earlier this month, will now look to enjoy more success after being handed the reins at Estadio Jose Alvalade until 2018.
"I want to be a champion at Sporting," Silva said. "The grandeur, the history, the culture, is something natural."
Sporting finished second behind fierce rivals Benfica this season, securing a place in the group stages of next term's UEFA Champions League.
