The 24-year-old striker spent two months on loan at Pride Park earlier in the season and Rams boss Nigel Clough remained keen on the player, whose signature he has now secured.
A delighted Rams manager Nigel Clough said: "Chris did really well whilst here on loan so we're pleased to get him signed up, and it's another important signing for us.
"He's a striker with different qualities to what we've already got, especially with his physical presence and ability to hold the ball up.
"We've admired him from afar for some time and monitored his progress closely, and once we got him in the building we knew he would fit in just fine with how we want to play and this group of lads.
"We can't wait to see him in action come the start August with a full pre-season behind him."
Martin becomes the Rams' second summer signing as the club have already agreed terms with Burnley keeper Lee Grant who, like Martin, will join the club on July 1st when the transfer window officially opens.