Republic of Ireland international McGeady joins on a three-year deal, having played under new Black Cats boss Simon Grayson on loan at Preston North End last season.
Vaughan, meanwhile, has put pen to paper on a two-year contract at the Stadium of Light, having scored 24 goals in 37 appearances for League One Bury in 2016-17.
Grayson told the official Sunderland website: "Aiden's career speaks volumes. He's been an exceptional player and was an outstanding performer at Preston last season.
"He was recognised by the league with Player of the Month awards and he already knows a few of the lads from his Everton days. He has the pace to take people on and carry us up the pitch, and he'll excite the supporters.
"James has good experience and he scored a lot of goals last year. He's a player who will come into the squad and give us something different because I think we were missing a striker with a physical presence – and he certainly brings that attribute. He's mobile, he knows where the goal is and he fits in with the ethos that we're trying to bring to Sunderland."
The fees paid for both players are undisclosed, although the sum for Vaughan's transfer is reported to be in the region of £900,000.