Ancelotti, who won the 2010 English Premier League in the first of his two seasons as Chelsea coach, avoided his former team in Friday’s draw.
Chelsea was paired with Slavia Prague, which shocked five-time champion Sevilla with a comeback late in extra time in the round of 16 on Thursday.
An all-Spanish pairing sees Villarreal play Valencia, and three-time runner-up Benfica will face Eintracht Frankfurt.
First leg games are played on April 11, when Arsenal will host Napoli. Return games are on April 18.
Ancelotti never won the Europa League, or the old UEFA Cup, as a player or coach though he has five European Cup or Champions League titles from his spells with AC Milan and Real Madrid.
With Napoli in a comfortable second place in Serie A, Ancelotti looks sure to lead the team back into the Champions League next season.
Arsenal and Chelsea, however, might need a path into the top-tier competition next season by taking the place reserved for the Europa League winner. Both are in a tight race for a top-four finish in the Premier League.
The London clubs avoided each other in the semifinals pairings that were also made on Friday.
Arsenal or Napoli were drawn to play Villarreal or Valencia, and Benfica or Eintracht Frankfurt would be at home first against Chelsea or Slavia Prague.
The final is on May 29 at the Olympic Stadium in Baku, Azerbaijan.