The one-cap Spain international was made the world's most expensive goalkeeper earlier this week as the Blues moved to replace Real Madrid-bound Courtois.
Kepa is highly rated in his homeland, where he has spent the past two years in Athletic Bilbao's first team, but he arrives in West London with limited grasp of the English language.
Rudiger was more than happy with Kepa's "confident" debut display, though, with Chelsea running out 3-0 winners away to Huddersfield Town on Saturday afternoon.
"I think he did well. He tried to speak as much as he can. He did well with that and we as defenders we needed to help him and we did that," the German centre-back told Sky Sports News.
"In general, it was a very good day. We all know Thibaut's quality, but Thibaut's not a Chelsea player anymore. I wish him good luck at Real Madrid, but now we have to concentrate on Kepa because he's our goalkeeper. In his work he's very confident.
"We're happy because to be honest our pre-season games were not that good. But today we can be more happy because we won the game. Three goals and a clean sheet. That's good for us.
"It's not always easy to adapt because it's a new style of play, but I think we did well. We moved the ball well and to have a good bench is always good."
Kepa made just one save all afternoon at the John Smith's Stadium.