"Bottas is the best man (for the job). I believe that he can drive as fast as Nico. I believe he can win the world championship," the Austrian, a retired triple champion, told Germany's RTL television.
"We can start the season in a very calm and confident manner with the pair of them," added the Mercedes team's non-executive chairman.
Mercedes announced the Finn's arrival from Williams on Monday, with the 27-year-old presented as a quick and experienced team mate for Britain's triple world champion Lewis Hamilton.
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Hamilton won 10 of the 21 races last year but was beaten overall by Rosberg, the rival he has measured himself against since they were boyhood team mates in karting and who won nine races.
The Briton, whose first title was with McLaren in 2008, beat Rosberg comfortably to the championship in 2015 and also prevailed in 2014.
Rosberg announced his retirement in December, five days after taking the title, in a surprise move that left Mercedes scrambling to secure a replacement with all the top drivers already under contract elsewhere.
Mercedes team boss Toto Wolff has had a long-standing involvement in Bottas's management, although he said that will now end, and was a former shareholder in Mercedes-powered Williams.
Hamilton, 32, will start the new season in Australia on March 26 as favourite to take a fourth title but Lauda said the mood at the team was relaxed because they again had two top drivers.
"We looked for a driver who fits our team. Until now we always had two top drivers who could fight for the world championship," he said.
"Nico and Lewis were a fine example of that, because they were fighting head-to-head.
"In the last three years we won everything there was to win. And this is why we decided to go with Bottas, as he brings experience and speed to the team.
"Both drivers can push as hard as they want, as always," continued the Austrian. "This has never changed at Mercedes and it will not change in the future."
(Reporting by Alan Baldwin, editing by Ed Osmond)
