Martin told BBC Radio Derby: "You have always got to expect the unexpected.
"I was training and I came into the training room and there was a phonecall saying Derby were interested, and I jumped at the chance."
Martin originally came through the youth ranks at MK Dons but signed for Liverpool in 2006, after impressive displays both for his club and various England youth sides.
He has been on loan at a number of clubs including Leicester, Leeds, Tranmere and Accrington Stanley.
"This season has been quite frustrating for me personally," added Martin.
"I have had a few loan clubs here and there but not really had many games. I am 24 now and I want to play."