DC United confirmed on Tuesday he will depart the club at the end of the 2019 MLS season:
Derby announced there will be the option of a further year in his contract.
Rooney, 33, joined the MLS side in June 2018 from Everton, penning a three-and-a-half-year deal.
He has largely impressed in the United States, netting 23 goals in 43 league appearances for the Washington, D.C. outfit.
"It's something which I want to stay involved in; [my coaching badges] are going well. I'm obviously still a player, and I want to continue to play. When the time is right I can go into coaching or management."
Rooney should be a major asset at Derby as they look to earn promotion to the Premier League.
He is no longer at the peak of his powers, but the former Manchester United forward has displayed his knack for goalscoring in MLS.
As United and England's all-time record goalscorer, Derby could hardly have hoped to add a player with more experience to their side.
Phillip Cocu was appointed as Lampard's successor, and Rooney will join his team of coaches as well as his playing staff.