The Brewers were light up front after losing Calvin Zola and Jacques Maghoma on free transfers earlier this summer.
Howe, 26, scored 16 goals for the Gulls last term and was said to be interesting a host of clubs.
The forward was keen to move further north, however, and Burton boss Gary Rowett was delighted to get his man.
He told Derbysport: "Rene is one that I've tried to stay in the loop about and I'd intensified my interest in the last two weeks.
"He had offers from Scotland, two from League One and I think at least one from the Championship, so it has been a real battle to get him and I'm really pleased that we have convinced him this is the place to come if he wants to further his career.
"I think he's a perfect striker for this division. He's big, he scores goals and he's a clever player, too."