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.
Bizarre Jose Mourinho statement aims to pre-empt punishment after Fenerbahce boss clashes with Galatasaray counterpart
'Andy Robertson has a decision to make as a player, where you either roll your sleeves up and give someone great competition or you accept decisions and say that your time is done.' Alan Shearer on the conundrum facing Arne Slot's Liverpool
