The Biancocelesti reached an agreement with the MLS club worth €15 million last week, and medical tests for Castellanos followed.
The Argentine will put pen to paper on a five-year deal with the Italian giants until 2028.
Castellanos spent the last season on loan at Girona, where he racked up 13 goals in La Liga and helped the Catalan club secure a tenth-place finish.
Most notably, he scored a quartet of goals in the 4-2 win against Real Madrid, thus becoming the first player ever to do so against Los Blancos this century.
Having created a huge impression in his only season in La Liga, the 24-year-old is now set for a more challenging task at Lazio.
Castellanos has been viewed as the long-term successor to Ciro Immobile, who continues to attract interest from Saudi Arabia.
It won’t be an easy feat for Castellanos to replace Immobile due to the Italian’s unmatched legacy at the capital club.
The Argentine is far from being a complete player, but Lazio manager Maurizio Sarri may help him fulfil his potential.
Sarri will expect more reinforcements as the capital giants are set to play in the Champions League after finishing second in Serie A last season.
The Biancocelesti are also keen on recruiting a midfielder in the transfer window, having lost their talismanic figure Sergej Milinkovic-Savic to Al Hilal.
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