Germany legend Voller, who scored 47 goals in 90 caps for his country and also played at the top level in Italy and France, spoke in glowing terms of Schurrle earlier this week.
The Bayer Leverkusen sporting director was sad to lose the 22-year-old forward to the Premier League but believes he can reach an elite level at Stamford Bridge under Jose Mourinho.
Voller told Express: "Andre can become an absolute world-class player. He needs to gain more ruggedness and has to become more forceful. That is important, most of all in England. If he gains on those areas, he will become a big player."
When told of Voller's comments, the Blues' £18million summer signing told reporters: "Hearing that makes me proud, but I know that I have to improve much.
"I want to improve, I have to work hard at my skills. It is an honour for me to play for this club and the only thing I want it to help the team with my qualities."
Schurrle was encouraged to make the move to London by former Chelsea midfielder Michael Ballack, who became a team-mate of his at Leverkusen in 2010.
"I played at Stamford Bridge with Leverkusen in the Champions League two seasons ago and that was a great feeling," added Schurrle, who was speaking from Kuala Lumpur where Chelsea will take on a Malaysian XI in their latest pre-season friendly on Sunday.
"Michael told me all the time this is a great club with great people, like a big family. He told me if I had to change, then I had to do this move to Chelsea.
"He also told me Jose is good for the players and convinced me he could make me a better player."
Schurrle would have preferred to move to Chelsea 12 months ago but his Bundesliga employers were reluctant to let him leave at that point.
"I always hoped this move would happen," said Schurrle. "It took a long time, and I'd wanted to come last year to Chelsea and it hadn't worked out.
"It wasn't my decision. It was the decision of Bayer Leverkusen: they didn't want me to go and I had to make the best of the situation.
"It was a missed opportunity, of course, but I said to myself I had to do my best in every match and every training session and it would come at another time. So it has proved. I had the contact all the time and now I'm very happy to be here.
"I had to do my work for Bayer Leverkusen and improve myself, and that's what happened. I wanted to be professional in all ways. The beginning was hard but afterwards it was okay. We had a good team."
Schurrle insists his price tag will not be a burden for him as he looks to make his mark in Chelsea's attack.
"Now I'm here, and for a lot of money," said Schurrle. "There's no extra pressure on me because of that, but it makes me proud that the club wanted me that much and paid the money. I will give them my best."