The 34-year-old striker has been playing in Canada for Vancouver Whitecaps but is back with the Scottish Championship side after being released from his contract.
Miller, who has signed a one-year deal, left Rangers to play in Turkey for Bursaspor in 2011 and also had a previous spell at Ibrox between 2000 and 2001.
He told Sky Sports News: "It has been on my radar for the last few years.
"It's no secret that I missed the place and I was always hoping that I could get that opportunity to come back, but it has taken a bit longer than I would have hoped.
"I am absolutely over the moon that it is done and I can come back and play at this fantastic club. I am a few years older but I feel great and fit. I still play the game the same way as I did before
"I left three and a half years ago but I'm sure the fans will see pretty much the same player that they will remember.
"The draw is the club, it is a simple as that. Leaving the MLS this summer was always going to be happening, so you have to try and cover all bases and first choice for me was always here.
"I never actively pursued anything else - it was the only place I wanted to come to. We worked hard to get it done with the manager and the chief executive.
"For me I would have had it done the minute I left Vancouver but it took a bit longer than I would have hoped. Now it's done, I am absolutely delighted and I'm looking forward to walking out in front of the fans."