The 29-year-old French left-back boosts the options of Marco Silva, who has guided the Cottagers to two wins out of five in the Premier League this season.
Kurzawa said: "I feel very, very happy to be here. It's a family here, everyone is very cool. I've watched every Fulham game this season and I can't wait to play with this team."
Willian became Fulham's second signing of transfer deadline day.
The former Chelsea and Arsenal attacker has agreed a one-year deal at Craven Cottage.
The 34-year-old had been playing for Corinthians back in Brazil, but left the club after receiving threats on social media.
Willian said: "I'm happy to be here, I'm happy to be back in the Premier League.
"Fulham is a special club, a club that wants to improve, that wants to fight for something bigger, so I'm here to help, and I can't wait to get started."