The Chile forward joined the Gunners from Barcelona last week in a deal worth around £30m.
Despite Sanchez having never played in the Premier League before, Jenkinson is convinced that the 25-year-old will adapt quickly.
"He is world class and they are the sort of players you want to see at the club," he told Sky Sports News. "The squad are buzzing as much as the fans, because if you are going to push on as a club and really compete for things, you need to sign top players.
"We have done that with him for sure - it is a fantastic addition. He's quick and direct, he can play up front and on the wing, and he is very dynamic. He will definitely fit the Arsenal style of play."
Arsenal get their Premier League campaign underway at home to Crystal Palace on August 16.