Crystal Palace v Sunderland: Team and injury news ahead of huge Selhurst Park clash
The Black Cats signed the Everton pair on Monday for a fee believed to be worth £7.5million but were not signed in time to face Tottenham Hotspur on Tuesday night.
They have both trained at the Academy of Light this week and will travel to London for the game.
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Hide AdSunderland are bottom of the Premier League ahead of the game, five points adrift of safety, with Crystal Palace two places and three points better off.
Speaking at his pre-match press conference, Moyes said: "Oviedo and Gibson will be in and around the squad.
"I've enjoyed having the new lads in because I know their character and I've worked with them in the past.
"I'm hoping they can come in and help us. Bryan replaces Patrick [van Aanholt] and Gibson reinforces the midfield. They're good lads."
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Hide AdDidier Ndong and Lamine Kone both starred against Spurs after returning to the Sunderland squad following Africa Cup of Nations duties with Gabon and Ivory Coast, respectively.
Moyes added: "The AFCON boys came straight back in but they did well, so let's hope they can continue their good form."
Centre-back Papy Djilobodji will serve the second of a four-game ban against Palace tomorrow.