In the final chapter of Yu-Gi-Oh!, Yugi has to defeat Atem to open the afterlife door, and they fight with their own deck. Short story, Yugi finally defeated his other self.
Since they bring their own deck, what happens to the other Yugi's deck when he disappears?
It was implied that Atem's (Yami Yugi's) deck and the Millenium Puzzle were left inside his tomb in Egypt.
But in the Movie, Yugioh: The Dark Side of the Dimension, it was shown that the Millenium Puzzle got reassembled again, but nothing happened.
In Episode 086 of Yugioh GX! (which is set years after YGO: TDSotD), Pegasus said that the Egyptian God Cards are gone.
Now, how did Kaiba summon Obelisk in YGO: TDSotD? The Power Vision disk didn't utilize actual cards. Instead, it created holograms from his mind.
Yugi uses his own deck.
TL;DR Atem's Deck is in his tomb.
It is implied that when the pharaoh went to the afterlife, he took the god cards with him. This was mentioned during Yu-Gi-Oh! GX by Pegasus and in the Yu-Gi-Oh! The Dark Side Of Dimensions movie by Diva. The god cards were in Atem's deck. And since we didn't see him taking out the god cards and leaving the deck behind to Yugi before he entered the gate to the afterlife, it is strongly implied that he took the entire deck with himself.
Not sure how Yugi found replacements for the cards in Atem's deck, but two options come to mind. Since Solomon Mutou is the owner of a game shop that sells cards, he probably helped Yugi to find the Dark Magician and Dark Magician Girl, along with any other cards that the pharaoh had in his deck. It is also possible that Pegasus sends replicas of the cards to Yugi along with some other cards like the different magician girls, as a sign of goodwill and friendship.
Actually, the deck that Atem had was returned to Yugi's deck, but only three cards were not in Yugi's deck and that was of course the Egyptian god cards. Therefore, the cards in Atem's deck excluding the Egyptian god cards were returned to Yugi's deck while Atem took the Egyptian god cards with him into the afterlife.