Klopp recently signed a six-year contract with the club.
Evans told the official Liverpool website: "I'm delighted and I'm sure all the fans are as well. It's great that he's put himself in a position where he wants to be there for a longer time.
"I thought he handled last season brilliantly. So far I think he's done everything in the right way, he's got a good balance.
"Of course, like every Liverpool manager, somewhere down the line the fans will want trophies - but I think he's the man to deliver."
Klopp led the side to two cup finals last season but the Reds could not manage to deliver their first piece of silverware since 2012. That said, there was enough reason for optimism in just under a season in charge of the club with no major signings made to improve the squad.
It seems that a lot is riding on Klopp to be a success at Anfield and that he has been instructed to implement measures for the club in the long-term.
With the Reds' boss shaping up for his first full season in charge, there is a certain degree of expectation of a good campaign given the lack of European football this term. A lot of emphasis from Klopp has been put on improving the side through training and he will have the time to do just that this time.
Evans has expressed his hope that Liverpool will manage to win some silverware this season after two near-misses last term, and one would feel it would be a huge step in the right direction for the side, as after recent seasons of coming so close, they will want to shake that particular monkey off their back.
Liverpool manager Juergen Klopp