The English transfer window slammed shut on Thursday, but EFL clubs are still permitted to seal loan deals up until the end of August.
That has resulted in the Black Cats pushing through the temporary transfer of Power, with the signing becoming permanent at the start of 2019.
Sunderland boss Jack Ross told the club's official website: "We wanted another midfielder in the squad and we wanted one who was a little bit different to what we already have.
"Max gives us a little bit more of a presence physically – box to box – and gives us more balance within the squad. He's got very recent experience when it comes to winning and being successful in this league and knows what it takes to get out of it."
Power scored 11 goals from 143 appearances during his three-and-a-half year spell at the DW Stadium.