Amorim, 36, penned a year-long extension which will take him to the end of the 2023/24 season.
Sporting did not disclose the details of the agreement but local media claimed the deal, including a release clause, was worth between 20-30 million euros.
Former Benfica player Amorim only joined Sporting, whose last league title came in 2002, from Braga last March.
They have not lost in the league this season and are nine points ahead of Sporting Braga, 10 in front of champions Porto and 13 points better off than Benfica.
Sporting have already won the Portuguese League Cup this season, beating Braga 1-0 in the final in January.
Standout matches today