The iconic London venue was chosen to stage the two showpiece contests after coronavirus restrictions meant Marseille was ruled out of hosting duties.
European Professional Club Rugby (EPCR) and the Rugby Football Union released a joint statement confirming the news on Saturday (AEST).
The Challenge Cup final will take place on 22 May (AEST), with the Champions Cup showdown the next day, and thousands of supporters will be welcomed to both.
"Fans are the lifeblood of European club tournaments and we are delighted to be able to welcome them back in a COVID-secure environment for this season's finals," EPCR chief executive Vincent Gaillard said.
"Twickenham has a storied history with club rugby's greatest tournament, and it will be a fitting venue to see silverware contested next month."
The identity of the four finalists will be known after the coming weekend, with Toulouse facing Bordeaux Begles and La Rochelle meeting Leinster in the premier continental knockout tournament, while there is a possibility of an all-English final in the Challenge Cup as Leicester Tigers take on Ulster and Bath tackle Montpellier.