Pearson, who also managed Hull City and Southampton, has signed a three-year contract at the former Premier League club, who just missed out on promotion from the Championship in last month's playoffs after finishing in fifth place.
The new Derby boss acknowledged at a news conference on Thursday that there would be comparisons with his experience with Leicester, whom he took from the second-tier to the Premier League.
"My main focus is about getting to grips with this job [at Derby] and using my experiences with previous jobs [to achieve it)," he said.
Under Pearson's guidance, Leicester narrowly avoided an immediate return to the English second tier in 2014-15 after winning seven of their last nine games.
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And last season, after Claudio Ranieri replaced Pearson, who was sacked following a clash with the club's owners, Leicester shocked the football world by winning the Premier League.
"It's a fantastic story. It's a story which gives a lot of clubs hope for the future," he said. "But with all due respect, I'm here to speak about being the manager of Derby County."
Pearson said he felt Derby were "a good fit". "There is an emphasis on developing the whole of the football club.
"For sure, we have aspirations to return to the Premier League, but the foundations are very solid here on lots of different levels."
Chris Powell, the former Derby player, who has managed Charlton Athletic and Huddersfield Town, will be Pearson's assistant.
Another Championship club to announce a new manager were Blackburn Rovers, who have appointed former Burnley and Bolton Wanderers boss Owen Coyle.
He succeeds Paul Lambert, who left at the end of the season, in which Blackburn finished 15th in England's second tier, and has signed a two-year deal, the club said on their website (www.rovers.co.uk) on Thursday.
(Reporting by Neville Dalton; editing by Clare Lovell)
