The announcement comes following the Foxes' relegation to the Championship on the final day of the Premier League season last month.
Turkish defender Soyuncu joined in 2018 from Freiburg and has featured over 100 times for Leicester, while fellow centurion Amartey made his first appearances for the club during their Premier League title-winning season in 2016.
Youri Tielemans is also among those leaving, having announced his exit on Instagram last week after spending four years with the club since joining from Monaco in 2019.
Captain Jonny Evans remains in discussions with the Foxes as his contract is set to expire this month, while an option has been exercised to extend Hamza Choudhury's contract to June 2024.
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