The 22-year-old made 30 appearances last term as the Bundesliga side finished 15th in the table, reached the last 16 of the DFB-Pokal and made the third qualifying round of the Europa League.
A Turkey international, Soyuncu made his senior debut for his nation aged 19 against Sweden in March 2016 and has since been capped a further 14 times.
Leicester announced the deal at 6pm, an hour after Thursday's transfer deadline, but Sky Sports News had reported that the transfer had been completed before then.
The former Premier League champions confirmed that Soyuncu has agreed personal terms, undergone a medical and signed a five-year contract, subject to a work permit being granted.
Leicester get their season underway on Friday night with a trip to Jose Mourinho's Manchester United.