The 21-year-old midfielder made just one first-team appearance for the Hammers, but had a successful loan at Northampton Town last season, losing just one of the 10 games he played.
"He's a young player with a lot of potential," said boss Nigel Clough.
"He wants to play first-team football and recognises that initially in order do that he needs to drop down."
Powell, who has featured for West Ham in their EFL Trophy side for the last four seasons, signed too late to make his Burton debut in Tuesday's League One home game with MK Dons.
"I'm here to learn some more," he said. "I'm hard working, box-to-box, very good on the ball and I like to create moments in the game that lead to goals."