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The 43-year-old former midfielder, capped three times for Portugal, replaced Leonel Pontes, who had been interim manager since Dutchman Marcel Keizer was dismissed on September 5.
Silas, whose given names is Jorge Manuel Fernandes, started the season at Belenenses before also being dismissed at the beginning of the month.
The club announced he had signed a contract until the end of the current season with an additional year as an option.
Keizer, who replaced another interim manager, Tiago Fernandes, last November, led Sporting to third in the Portuguese league last season.
This campaign has started badly. The club is seventh in the table after six matches with just two victories and lost their opening Europa League fixture to PSV Eindhoven.