Turkey's Fenerbahce, who like the Swiss champions Basel are in a European semi-final for the first time, will play twice European champions Benfica in the other tie.
Basel knocked Tottenham Hotspur out of the tournament in the quarter-finals and also eliminated Manchester United in the Champions League group stage last season.
"We have quite a good record against English teams," Basel president Bernhard Heusler told Reuters. "We are still a small Swiss team in the eyes of the English fans, but that doesn't matter, I like to be the underdog.
"It's fantastic for us. As I boy, I admired English football and Tottenham Hotspur, players like Glenn Hoddle.
"People ask me in Switzerland what I learned most and I said the sportsmanship, the way they treated us," he added.
"In Switzerland, it's the opposite. When a team loses, the president or club representative starts to blame referees or whatever.
"The English congratulated us, they didn't talk about the referees or penalties or non-penalties, they just said that we were the better team."
Chelsea are bidding to become only the fourth team to win all three of UEFA's major club competitions.
They won the old European Cup Winners' Cup in 1971 and 1998, as well as last year's Champions League, and would emulate Juventus, Ajax Amsterdam and Bayern Munich by adding the Europa League to their collection.
Basel, who have already played 18 European matches this season in an odyssey which began last July in Estonia, and Fenerbahce will play their first legs at home.
