The deal to take the Poland international to the Ramon Sanchez Pizjuan Stadium from Ligue 1 outfit Reims was finalised on Wednesday after the 24-year-old completed a medical on Monday.
Krychowiak will now remain in Spain until 2018 and is set to join his new team-mates for a pre-season friendly in Lyon later on Wednesday.
A statement on the Liga club's official website read: "Krychowiak is now officially a Sevilla player after signing his four-year contract.
"[He] immediately leaves for Lyon with his new team-mates.
"The player arrived on Monday to undergo a medical and finalise te contract. The Pole even got orders from [head coach Unai] Emery in training yesterday."
Having started his career at Bordeaux, Krychowiak moved to Reims on a full-time deal in June 2012 after previously playing for the club on loan.