Mercedes announced on Thursday morning that Hamilton would be joining them on a three-year deal from the start of the 2013 Formula One season, ending a 14-year association with McLaren.
Hamilton will replace Michael Schumacher at the German team, with Mexican Sergio Perez - currently with Sauber - stepping in for the Briton at McLaren.
McLaren team principal Martin Whitmarsh warned Hamilton that leaving for Mercedes will prove to be a mistake, but three-time former world champion Lauda - who held talks with a pragmatic and apparently emotionless Hamilton last week - said the 27-year-old was eager to start a new chapter.
"I spoke to him a couple of times, but I didn't have to convince him much," the 63-year-old told BBC Radio Five's Sportsweek programme. "He had a clear plan and I didn't have to convince him of anything.
"I can honestly say I was impressed with his approach to things - very pragmatic, no emotions whatsoever. The real discussion was, 'why should I leave a competitive car where my life is easier in the future?'
"My argument was, 'if you're looking for a new challenge then frankly the Mercedes team is one'. Thinking the other way round, if Michael Schumacher could not get the Mercedes team - for three years running - up front and you next year are doing much better, this makes a huge impact on your personality and people will rate you much higher than you are rated now."
He continued: "The money discussion I was not really involved in. The money was not really the case. The offer was very close to the one of McLaren. In the end it was that he looks for a new challenge.
"I understand him because if you drive six years for same the team and for the same people you get used to each other. It works for him because he won one championship and he is winning races, but nevertheless a new challenge with new people... you learn different things and different approaches - it's something that for a competitive guy like Lewis was very interesting."
Lauda has no doubt about the 27-year-old's speed and quality, but insisted there was no number one driver in the Mercedes team.
"I think he is, (even) in a bad car, the best driver in the world because he's unbelievably quick," Lauda said. "He makes no compromise. So if Hamilton would join the team next year, which he is, I can tell you he will make a big move forward on speed."
He added: "There's no number one and number two. There's enough money for Mercedes that they can prepare two cars exactly the same way.
"And what I really look forward to is that Hamilton will push Nico Rosberg to go quicker and Nico will push Hamilton to go quicker - and this is really all you need in a team."