Friday's draw saw Jose Mourinho's side handed a semi-final showdown with the current La Liga leaders, who caused a Champions League upset by knocking out compatriots Barcelona.
Chelsea started the week as outsiders having lost their first leg 3-1 to Paris Saint-Germain, but the Blues overturned that deficit at Stamford Bridge to clinch a place in the last four of Europe's elite competition.
Ramires believes there is little to choose between the teams ahead of the semi-finals and acknowledged both will enter the final four buoyed by their recent success.
"This is the time when everyone respects each other and nobody wants to choose an opponent," he told Globo Esporte.
"What makes our matches against Atletico Madrid special is that both teams are very confident at the moment after what happened in the quarter-finals.
"Atletico Madrid eliminated Barcelona, who are always favourites in the competition, while few people believed we would reverse the deficit against PSG. I think it will be two tightly-contested matches between two teams full of passion."
Ramires holds fond memories of Europe's premier competition having scored against Barcelona as Chelsea reached the Champions League final in 2012, when they beat Bayern Munich on penalties, but insists it is time to write more headlines.
"I had magic moments last time I played in the Champions League semi-finals," he added.
"It's impossible to forget the goal I scored against Barcelona, it really marked my life, but now it's the moment to try to build a beautiful new story.
"I'll give my best on the pitch to have more good things to remember from these matches."