Tournament organisers European Professional Club Rugby (EPCR) announced the Heineken Champions Cup and European Challenge Cup finals at the recently opened 62,000-seater stadium.
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It will be the seventh European Cup final to be played in England, and the first to held in London other than at Twickenham.
The stadium is due to host Premiership Rugby and NFL games as well as Spurs fixtures next season.
“We are excited to have been selected to host this prestigious weekend, the pinnacle of European club rugby, in 2021, and to have this opportunity to welcome EPCR and rugby fans from around the world to Tottenham to experience our new home,” Spurs chairman Daniel Levy said.