The 22-year-old attacker signed a five-year contract with the Blues on Tuesday after Chelsea agreed a fee of around £18m with Bayer Leverkusen earlier this month.
Chelsea booked their place in next season’s Champions League thanks to a third-place finish in the English top flight.
And Germany international Schürrle is desperate to help his new club challenge for Europe’s top prize under new manager José Mourinho.
“The Champions League is the greatest competition in elite football so I’m really looking forward to it,” Schürrle told Chelsea’s website.
“I’m hoping we can emulate the Chelsea side from two seasons ago, but we’ll see. I’m just happy to be involved in the tournament.
“I definitely think they [the English teams] have the quality and the players to be a serious threat in the Champions League.
“Last season Borussia Dortmund and Bayern Munich did very well, they are both great teams, but this time I hope it will be different. Premier League teams are always massive contenders to win the trophy.”