Pope scored 10 goals for the Alex last season but could not prevent them from suffering relegation to League Two, where he now finds himself with the Millers having penned a three-year deal.
He told Crewe's official website: "Crewe is a great club and they improve you as a player. They never stand in your way and I have nothing but respect for them."
The 23-year-old added: "I wasn't really looking to move on and no-one at Crewe forced me out or made me feel unwanted.
Rotherham made an enquiry and I felt it was in my interest to go and speak to them.
"I just felt it was the right time for me to move on and give myself a new challenge."