He added: "I worked with the manager Walter Smith and assistant manager with Scotland.
"I get on really well with Walter and Ally both on and off the field and I felt they got the best out of me for the national team."
Miller has scored 11 goals in 37 appearances for Scotland and said he was confident of making an impact at Ibrox.
"I definitely feel I'm coming here a far better player than when I left first time around," he added.
Smith said he was delighted to secure Miller's signature, adding: "Kenny has matured into one of the best strikers Scotland has and I believe he'll be a terrific addition to our squad."
Miller enjoyed mixed fortunes in his previous stint with Rangers under Dick Advocaat after moving from Hibernian in June 2000 for �2m.
Wolves spent �3m to take the striker to Molineux, where he spent five seasons, before Gordon Strachan brought him to Celtic on a free transfer in July.
However, the forward found the net only 11 times in just over a year in the East End of Glasgow and was transferred to Derby.
Miller scored six goals in 33 appearances for Derby as they dropped out of the Premier League in England following a miserable campaign.
Derby manager Paul Jewell said: "I believe this deal is good for all parties involved."
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