Werner has left Leipzig for the Blues and will play alongside Adams' United States teammate Pulisic in attack.
"It's sad to see one of your best players go," Adams said. "But it's also sad to see a good person go because he's a really good guy.
"He will cause problems for any defence in the world with his speed and be dangerous in front of goal.
"I'm really looking forward to seeing him play there and cause problems for all the teams there."