Although Gameiro was considered a viable option both out wide and in attack, the pre-season arrivals of Gelson Martins, Nikola Kalinic and Thomas Lemar saw him fall even further down the pecking order, and Atletico have reportedly managed to recoup €16m (£14m/$18m) for the 31-year-old.
Gameiro has become Valencia's second attacking reinforcement in quick succession following the loan arrival of Michy Batshuayi and he plans to be available to face Atletico as his new side get their La Liga campaign started on August 20.
"Perhaps," Gameiro told a news conference when asked if he will be ready for the visit of Atletico.
"I have a little time left to get there [in terms of fitness]. I have a week to be here and prepare for the game."
According to speculation, Simeone and Atletico were reluctant to sell Gameiro, particularly to a team which will likely be a direct rival of theirs in the top four this season.
But in securing the switch, Gameiro finds himself somewhere he has wanted to be for quite some time.
"It was not easy, but as the president has said, it has long been clear in my head [that he wanted to join Valencia]," Gameiro said. "Now I'm here and I'm very happy.
"A long time ago I wanted to come here, but because of club problems it couldn't be. Then there was no option and I went somewhere else.
"The coach [Marcelino Garcia Toral] told me that he wanted to work with me for a long time. When the coach tells you that, it gives you a lot of confidence to come. I will work hard to try to do many great things here."
Gameiro has signed a three-year deal at Valencia.