The London club finished top of the first phase in the league stage of the competition, the only side to win all six matches, and are favourites to go all the way and win the trophy.
They will go to the Danish capital for the first leg on March 6, before hosting the return at Stamford Bridge a week later.
Copenhagen finished 18th in the 36-team league phase, notably beating Hearts of Scotland, before eliminating German Bundesliga side Heidenheim in extra-time in the play-off round.
The Danes got to the last 16 of last season's Champions League before losing to Manchester City.
Chelsea won 2-0 on aggregate when the teams met in the Champions League last 16 in 2011.
If Enzo Maresca's side win, they will advance to a quarter-final against either Molde of Norway or Legia Warsaw of Poland.
Chelsea are hoping to go all the way to the final in the Polish city of Wroclaw at the end of May and they cannot face Fiorentina until then.
The Italians, who have appeared in the last two Conference League finals, are probably the biggest threat remaining to Chelsea in the competition.
The side from Florence will face Panathinaikos of Greece in the last 16, with the winners of that taking on either Celje of Slovenia or Lugano, the current Swiss Super League leaders, in the quarter-finals.
Potential semi-final opponents for Chelsea are Pafos of Cyprus, Djurgarden of Sweden, Borac Banja Luka of Bosnia and Herzegovina, and Austrians Rapid Vienna.
Last 16 draw
Quarter-final draw
Real Betis or Vitoria SC v Jagiellonia or Cercle Brugge
Celje or Lugano v Panathinaikos or Fiorentina
Copenhagen or Chelsea v Molde or Legia Warszawa
Pafos or Djurgarden v Borac or Rapid Vienna
Semi-final draw
Real Betis or Vitoria SC or Jagiellonia or Cercle Brugge v Celje or Lugano or Panathinaikos or Fiorentina
Copenhagen or Chelsea or Molde or Legia Warszawa v Pafos or Djurgarden or Borac or Rapid Vienna