Christensen, 26, has agreed on a contract at Camp Nou until 2026 after his Chelsea deal expired last week. Christensen became Barcelona's second signing of the day, following the arrival of AC Milan midfielder Franck Kessie.
At a point, Chelsea were leading the game but their inefficiency in defensive skills led the match to end in a draw.
The Blues take on the Red Devils in the FA Cup final on May 19 at Wembley Stadium.
The duo face a race against time to be fit for Sunday's clash at Stamford Bridge.
