The 31-year-old spent four years at Kenilworth Road, scoring 72 goals in 183 games, winning two promotions as Town went from League Two to the Championship.
Collins then went to the Bluebirds when his contract expired, but ended up struggling in Wales, finding the net just three times in 30 appearances for the Bluebirds.
The Irish international has now penned a two year deal at Pride Park, as speaking to the Rams official website, he said: “I’m really excited and I’m desperate to get back playing football again and scoring goals.
“I’m really excited to be here.
“I spoke to the manager (Steve Morison) at Cardiff last year and he explained to me that he wanted to go down a different route which is fine.
“It’s football and it happens and this move happened during the summer.
“There were talks and interest and I spoke to the manager about the move.
“A lot of players I know have signed for the club so that was a big factor and we’ve built a great squad here so far so I’m excited to come here and be a part of it.”
With Derby relegated out of the Championship last term, Collins is now hoping to experience going up for a sixth time in his career, adding: “I’ve had five promotions as a player, four from League Two and one from League One.
“To have any promotion on your CV is good but to have five I’m really proud of that so hopefully I can make it six this year.
“There is no going away from the fact that I was in my most successful time in my career at Luton.
“I signed there in League Two and left there in the Championship so to get back-to-back promotions there was great.
“I scored a lot of goals along the way on that journey.
“It was a tough decision to leave Luton but it was time for a new challenge when I moved to Cardiff, but I loved my time at Luton and scoring goals for a good club is great.”