The two sides agreed a fee and May travelled to Glanford Park for talks before penning a two and a half year deal.
May, 23, had a loan spell at Glanford Park earlier in the season, and he impressed as a target man, showing some neat touches.
He played in Millwall's FA Cup replay with Walsall, earning the Lions a route into Round four with, what turned out to be his last goal for the Londoners.