The Barclays Premier League side, who beat Bayern Munich to the Champions League crown last season, will first face the Swiss opposition away from home on April 25 before the second leg at Stamford Bridge on May 2.
Fenerbahce, who beat Lazio 3-1 on aggregate to progress to the final four having lost their two previous European quarter-finals, will play Benfica in the other semi-final match.
Basle, who needed penalties to overcome Tottenham after their quarter-final was tied 4-4 after the two legs, will face a Blues side who secured their path to the final four with a 5-4 aggregate win over Russian side Rubin Kazan.
Portuguese side Benfica, who defeated Newcastle to leave Chelsea the sole English club left in European competition, have been rewarded with a showdown with Istanbul-based Fenerbahce on the next step to the final in Amsterdam on May 15.
The draw, held at UEFA headquarters in Nyon, also decided that the winners of Fenerbahce and Benfica will be classed as the home team in next month's final.
Source: PA
Source: PA