Vietto, 20, scored 18 goals in 72 league appearances for Racing Club, and has confirmed his switch to La Liga.
The Cordoba-born forward played under now Atletico Madrid boss Diego Simeone at Racing, and has been reportedly on the wishlists of Liverpool, Arsenal and Leicester City in recent months.
An Under-20 international with Argentina, Vietto will be unveiled at El Madrigal at 1300 local time (1100 GMT) on Tuesday.
It will be a case of one Argentine in, and one out, for last season's sixth-placed outfit, with defender Mateo Musacchio's departure confirmed recently by coach Marcelino.
Musacchio is set to join Premier League club Tottenham, after 139 league appearances for Villarreal.
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