"Silva was today informed of his dismissal with just cause, as it has not been possible to come to terms with him," Sporting said in a statement on the securities market regulator CMVM's website.
Both Sporting and Benfica are listed companies and have to report new contracts and sackings to the regulator. Sporting's shares soared almost 18 percent on Thursday, while Benfica's stocks fell 5.6 percent.
Local media said Jesus would switch to Sporting after a salary dispute.
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Benfica had been trying to cut Jesus's wage, which was the highest for any coach in Portugal, Expresso newspaper said on its website. The report also said Jesus's move to Sporting was backed by the club's Angolan shareholder Alvaro Sobrinho.
Jesus has managed Benfica since 2009, but also has a personal connection with Sporting where his father, Virgolino, played in the 1940s.
Sporting on Sunday won the Portuguese Cup -- their first trophy in seven years -- in a dramatic fightback against Braga.

Benfica's coach Jorge Jesus reacts during their Portuguese premier league soccer match against Guimaraes

Image credit: Reuters

Sporting have to sack their coach Marco Silva before the move can be announced, local media said. The announcements have to be made via the securities market regulator CMVM since both clubs are listed companies.
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Sporting on Sunday won the Portuguese Cup, their first trophy in seven years, in a dramatic fightback against Braga.
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