Edinburgh will play in the last 16 of the former, while Glasgow Warriors will be in the draw for the same stage of the latter.
Both tournaments will resume on the weekend of April 2/3/4 and the knockout stages will continue in April and May with quarter-finals, semi-finals and the two finals, which will both take place in Marseille.
The draw for the knockout stages will take place on Tuesday March 9.
The group phase of the two tournaments had to be cut short in the autumn due to outbreaks of Coronavirus at several clubs which caused matches to be cancelled.
The competitions have now been revamped, with a round of 16 added. Teams who won their two group games are to be rewarded with a home tie in the first knockout round. Edinburgh won one and lost one.
Glasgow Warriors lost to Exeter Chiefs in their opening Champions Cup match and were then forced to forfeit their next match against Lyon due to a Covid-19 outbreak. Glasgow now drop into the Challenge Cup last 16.
A statement from organisers European Professional Club Rugby (EPCR) said: “Regarding the Heineken Champions Cup, the eight highest-ranked clubs in Pool A and the eight highest-ranked clubs in Pool B at the time of the suspension of the tournament have qualified for the Round of 16.
“For the purposes of the draw, clubs from the same league cannot be drawn against one another, however, clubs from either pool can be drawn against one another.
“A further agreed key principle of the Heineken Champions Cup draw will ensure that clubs which have won both pool stage matches on the pitch – ie. where results were not impacted by Covid-19 – will play at home in the Round of 16.
“Therefore, Racing 92, Leinster Rugby, Wasps, Bordeaux-Bègles and Munster Rugby will each be guaranteed a home fixture.
“The clubs which are not drawn against either Racing 92, Leinster, Wasps, Bordeaux-Bègles or Munster will have their opponents, and whether they will be playing at home or away, determined as part of the draw.
“Regarding the Challenge Cup, the eight highest-ranked clubs from the preliminary stage at the time of the suspension of the tournament and the eight clubs which have not qualified for the knockout stage of Heineken Champions Cup will compete in the Round of 16.
“For the purposes of the draw, clubs from the same league cannot be drawn against one another, however, Challenge Cup clubs and Heineken Champions Cup clubs can be drawn against one another.
“Clubs which have won both Challenge Cup preliminary stage matches on the pitch - ie. where results were not impacted by COVID-19 – will play at home in the Round of 16.
“It has also been agreed that open draws will take place to determine the quarter-finals in both the Heineken Champions Cup and Challenge Cup, allowing for the possibility of matches between clubs from the same league.”
2020/21 KNOCKOUT STAGE QUALIFIERS
Heineken Champions Cup: Racing 92, Leinster Rugby, Wasps, Bordeaux-Bègles, Munster Rugby, Lyon, Toulouse, La Rochelle, Scarlets, ASM Clermont Auvergne, Bristol Bears, Exeter Chiefs, Edinburgh Rugby, Gloucester Rugby, RC Toulon, Sale Sharks.
Challenge Cup: London Irish, Ospreys, Leicester Tigers, Cardiff Blues, Zebre Rugby Club, Agen, Benetton Rugby, Newcastle Falcons, Ulster Rugby, Connacht Rugby, Northampton Saints, Bath Rugby, Montpellier, Dragons, Harlequins, Glasgow Warriors.
Knockout Stage Draws: Tuesday 9 March
Rounds of 16: 2/3/4 April
Quarter-finals: 9/10/11 April
Semi-finals: 30 April – 1/2 May
Challenge Cup final: Marseille - Friday, 21 May
Heineken Champions Cup final: Marseille - Saturday, 22 May