The 30-year-old rejoined the Rams for a fee of around £2m on Saturday night, 12 years after leaving the club for spells with Tottenham Hotspur and Hull.
An academy graduate at Pride Park, Huddlestone is happy to be back at his old home after seeing his contract with the Tigers enter its final 12 months, with fresh terms not offered until Derby had made a move.
"Once I got wind of the serious interest from Derby, it was a no-brainer," he told County's official website.
"Once Derby activated [a buyout clause in my contract], Hull decided to come with an offer then. If Hull had come with that maybe three weeks ago, before Derby were interested, I would have signed it happily and stayed there."
In response, Hull vice-chairman Ehab Allam told City's website: "We recently met with Tom's representatives, prior to receiving the offer from Derby to discuss a new longer-term deal on improved terms.
"I feel this stated our intention to keep Tom at the club, but ultimately the decision to leave was down to Tom and his representatives. We would like to wish Tom well for the future, and thank him for his efforts."
Huddlestone joined Hull from Tottenham in 2013, going on to make 112 league starts for the Humberside outfit during that time.