Officials close to the negotiations told Efe that the final details of the transfer were finalised on Friday night in the training camp of Sevilla in Germany, and Gameiro will travel to Madrid on Saturday to undergo medical tests before joining Atletico.
Vietto will join Sevilla on loan for one year with a permanent purchase option in June 2017 for 20 million euros ($22.3 million).
Atletico also agreed to pay another four million euros ($4.4 million) in variables in Gemeiro's four-year deal.
Gameiro, 29, has appeared with France and was previously at Strasbourg, Lorient and Paris Saint-Germain before moving to Sevilla in the summer of 2013.
During his three seasons at Sevilla, Gameiro claimed three titles of the UEFA Europa League and scored 67 goals in 144 games.
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