Lazio did not give any details but Italian media said he had joined on a five-year contract for a transfer fee of about 15 million euros plus five million in add-ons.
Castellanos spent last season on loan at Spanish LaLiga side Girona, where he netted 14 goals in 37 matches.
He hit the headlines when he scored four goals against Real Madrid in a 4-2 victory in April - the first player in 75 years to achieve such a feat against them in LaLiga.
Lazio finished second to claim a Champions League spot.