They have also brought in 24-year-old Lukas Rupp from Paderborn on a three-year-contract to boost their midfield.
No financial details were disclosed for either deal.
The 28-year-old Tyton, who last season played on loan for Spain's Elche, has signed a two-year deal, Stuttgart said.
"Przemyslaw Tyton convinced (us) with his qualities in Spain's Primera Division," said Stuttgart sports director Robin Dutt in a statement. "We monitored him intensively and had a complete picture of his abilities."
Tyton, who is 1.95 metres tall and has 13 caps, has been signed to replace Ulreich, with the former Bundesliga champions determined to avoid a second consecutive relegation scrap.
(Reporting by Karolos Grohmann; Editing by Ken Ferris)
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