"I've always wanted to manage a club with a big tradition and history like Derby County, so this is a huge opportunity," Lampard told the club's website.
Lampard's move means that he did not wait long to follow former England team mate Steven Gerrard into management, with the ex-Liverpool midfielder taking charge at Scottish side Rangers earlier this month.
"We want to build on the club's top-six finish in the Championship last season, while at the same time bringing through some of the excellent youth and academy talent we have at Pride Park," Lampard added.
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"I'm delighted to have someone of Frank's calibre as our new manager," Derby executive chairman Mel Morris said.
"Few players have achieved what Frank has in his career. He's a winner, a leader who knows what it takes to succeed and who has the character and charisma to be a fantastic manager."
Rowett guided two-times English champions Derby to the playoffs last season, where they were beaten 2-1 on aggregate by Fulham, who went on to earn promotion to Premier League.
The 44-year-old left Derby to take charge of Stoke City, who were relegated from the Premier League last season.
(Reporting by Shrivathsa Sridhar in Bengaluru; Editing by John O'Brien)
