The Wales boss was awarded the role a week ago ahead of the 2013 tour in Australia after a successful spell in charge of the Red Dragons.
Dawson, who featured at scrum-half for the Lions, believes that Gatland will do well in his new post.
"I think it's the right appointment, the Lions committee have absolutely nailed it," Dawson said.
"Maybe for once in goodness knows how long there's very little controversy."
The Lions will play three Test matches against the Wallabies as well as seven tour friendlies, including a game against the Barbarians in Hong Kong.