The 28-year-old arrived for £2M plus add-ons as Town sought cover following Christian Walton’s injury and Aro Muric’s struggles.
Palmer, who spent time on loan at several clubs, had been with West Brom since the age of 14.
“Hectic, but that’s football,” Palmer told TownTV about deadline day.
“I think it’s an exciting time for me to embrace a new challenge.
“Of course, when you spend that amount of time somewhere it’s obviously going to be a hard decision, but I felt it was the right time to try a new thing and take a new pathway. I think that’s all part of life.
“I’ve had a great time, I’ve met some great people at West Brom and I wish them all the best. I’m looking forward to a new challenge here.”
Reflecting on his new side, he added: “You see it as a club that’s going places and on a good trajectory and everything that I’ve heard about the manager is positive.
“Coming here and being part of a group that’s achieved a lot of things in a short space of time is really exciting.”