Former Portugal defender Pereira had three spells at Sporting as a player, making 154 appearances with his last season under Amorim in 2020-2021 when they won the title.
The 40-year-old, who led Sporting's Under-23 and B teams, takes over a club in impressive form with 16 wins and a draw this season.
"As a player, Sporting gave me a lot, allowing me to play for the national team, join one of the best leagues in the world and return home twice," Pereira, who also played in Spain, Germany and Turkey, told a news conference on Monday.
"I only repaid them with a Super Cup and a national championship, which felt more like their gift to me. That's something I regret, so as a coach I'd like to repay them with more titles because Sporting deserve it.
Pereira had kind words for his predecessor, who brought him back to the club in 2021. Amorim will take charge at United after the November international break.
The 39-year-old Amorim enjoyed a successful four-year tenure, guiding Sporting to their first league title in 19 years in 2021 and reclaiming the trophy last season.
Sporting lead the Primeira Liga with a perfect 33 points from 11 games, six ahead of Porto, and are second in the Champions League, two points behind Liverpool.
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