The 36-year-old, who has a doctorate in law, also officiated the Blues' incredible last-16 second-leg comeback against Napoli.
Brych, who is renowned as a disciplinarian, controversially sent off Manchester United captain Nemanja Vidic in the Premier League champions' group-stage fixture with Otelul Galati in Romania.
Chelsea's previous clashes with Barcelona since 2005 have been dogged by refereeing controversy.