The west Londoners brought a 1-0 lead into the second leg at Stamford Bridge and Hakim Ziyech increased their advantage when he slotted Timo Werner's cross past the Atletico goalkeeper Jan Oblak inthe 34th minute.
Atletico boss Diego Simeone said his side would be on the front foot for the clash but despite the presence of Luis Suarez and Joao Felix they were unable to breach the Chelsea rearguard who had conceded only two goals in the 12 games of Tuchel's reign.
"The most important thing is we deserve this," Tuchel said. "They play with a special bond and results like this give you a certain edge to achieve special things.
"I'm sure no one wants to play against us. This will be a difficult challenge ... But no need to be afraid. We take what we get."
Emerson Palmieri scored Chelsea's second in stoppage time to complete a 3-0 aggregate win and seal a berth in the last eight for the first time since 2014.
Big guns
There they will face the likes of Paris Saint-Germain, holders Bayern Munich as well fellow Premier League sides Liverpool and Manchester City.
Real Madrid, Borussia Dortmund and Porto also lie in wait in the draw on Friday.
"We need to improve in counterattacks," Tuchel added. "We have to be more forward thinking, use our speed and exploit spaces. We must be more clinical and precise."
Atletico will return to Spain to pursue their first La Liga title since 2014 while Chelsea, who are fourth in the Premier League, host Sheffield United in the FA Cup quarter-finals on Sunday.
