Video report by ITV News Correspondent Damon Green
England's record goalscorer will join the Rams in January 2020 in a player-coach capacity, with his contract running until 2021.
The 33-year-old, who joins Derby from DC United in the US, said his family's situation was "first of all" in his thinking.
He said: "Certainly for my eldest boy it’s a crucial time in his school period so of course that’s first of all, that’s the most important thing to me.
"It’s something that we looked at, and also the opportunity to come back here and play and as, I’ve said before, be part of the next transition in my career.
"It wasn’t solely on family, it was a few factors which led me to come back here."
The former Manchester United forward has the option to extend his stay for a further year at Derby.
Rooney, who will wear the number 32, will play out the rest of the MLS season before joining the Rams.
He said: “I am very excited about the opportunity that Derby County have provided me with.
“I am looking forward to joining Phillip Cocu, his coaching staff and the first-team squad from the start of January. I am sure I can make a big contribution and can’t wait to meet everyone, especially the supporters.
“I am equally excited to begin my coaching career at Derby County working with both the first team and Academy.
“I must also take this opportunity to thank DC United, their owners, executives and supporters who have been superb to work with. I want them to know that I will give my all in support of our push for the play-offs.”
During his professional career for Everton, Manchester United, DC United and England, Rooney has made over 700 appearances and scored over 300 goals.
Derby manager Phillip Cocu said: "Wayne Rooney is an extremely talented and top-class footballer.
“It is an exciting prospect for him to be joining Derby County and he can bring so much to this squad, both on and off the pitch. He has enjoyed a wonderful career, both in club football and for England, and he still has so much to give as well.
Derby fans react to Wayne Rooney signing
“His credentials speak for themselves. But to have a player with his leadership, skill, experience, character and work ethic will be huge for us. He knows what it takes to succeed as a player and I have no doubt he will have a positive impact right across the club.
“The inspiration and motivation this can generate is massive for all of our players from the first team right through to the youngsters in the Academy. It is entirely in keeping with, and in support of, the club’s philosophy and approach.
“I am looking forward to working with Wayne from the start of next year and welcoming him to the club.”