The Brewers boss told BBC Radio Derby: "I'm very excited by the signing.
"He's a player I've admired for some time. I'm delighted we've finally got pen to paper and made it a done deal."
He added: "He's going to be an important member of the squad because he's got very good quality, particularly from set pieces, plus the fact that he can play several positions was a great selling point, so I'm very excited.
Palmer has had spells with Notts County, Wycombe and Walsall.
The former Derby trainee was predominantly used as a left-sided midfielder at Gillingham but can also play in either full-back position.
Palmer said: "I think for me and my family, it's been a good opportunity to come back home and I'm really looking forward to working with Paul because I know him and quite a few of the other players here so I'm quite excited about the future.
"A few people might be surprised to see me leaving Gillingham, but if anyone knows me, they'll know I've only done it for reasons that are going to be justified and that's really because I want to be nearer home and I'm excited by a new challenge.
"Obviously it was disappointing for us [Gillingham] not to have made the play-offs last season but I'm looking for a fresh start and this is a good opportunity for me to do that."
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