Pereira, who was hired on November 11 following the departure of Ruben Amorim to English giants Manchester United, was sacked by the club on Thursday.
He had three spells at Sporting as a player and took over as coach with the team in first place in the Portuguese league and in second place in the revamped Champions League.
Sporting are now second domestically, a point behind Benfica, and in 17th place in the Champions League with two matches remaining.
The top eight go directly to the last 16 and the teams placed ninth to 24th go into the play-offs.
Pereira won three of his eight games in charge, and included in that period was a 5-1 loss to Arsenal in the Champions League.
"Joao Pereira came in at a time when everyone knew there was an extremely tough challenge ahead," Sporting president Frederico Varandas said.
"Unfortunately, we came to the conclusion that it was not working out."
Varandas said the appointment of Borges, who left his role at Vitoria de Guimaraes, "marks a new chapter."
"He is a coach that we have had on our radar for over a year, who has progressed throughout his career," Varandas said.
"Sporting are alive on all fronts, fighting for all the trophies available, and will continue to fight."
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