The 23-year-old will become the club’s record transfer at £15million, after a wonderful loan spell at Eibar last season. Baston score 18 goals from 36 La Liga fixtures.
It was the fifth year running that the Spaniard spent the season on loan away from parent club Atletico Madrid, and it seems Diego Simeone is finally ready to permanently lose the youngster.
The Swans have lost plenty of firepower this summer, with Bafetimibi Gomis, Eder, Alberto Paloschi and Andre Ayew all departing the Welsh side across the transfer window.
Baston will join fellow Spaniard Fernando Llorente, who has completed his move to the Liberty, and both should be available for their trip to Burnley on Saturday in their Premier League curtain raiser.
However, the club could be losing club captain Ashley Williams, with the defender looking set to finalise a move to Everton.