Argentina forward Giovanni Simeone. AFP
The 27-year-old Simeone _ the son of Atletico Madrid coach Diego Simeone _ has already taken part in his first training session with his new teammates.
Napoli has the option to sign Simeone on a permanent basis at the end of the season.
Simeone scored 17 goals in 35 appearances for Verona last season. He was on loan from Cagliari and the club signed him on a four-year contract only in June.
He also played for Fiorentina and Genoa in Serie A after moving to Italy from Argentina in 2016.
Napoli, which is one of the title contenders, kicked off the season with a convincing 5-2 win over Verona on Monday. Simeone was not in the Verona matchday squad.
Another new signing, Khvicha Kvaratskhelia, shone with a goal and an assist.
Napoli finished third last season but there were question marks over how it would perform following the departure of several key players including captain Lorenzo Insigne, all-time leading scorer Dries Mertens and defender Kalidou Koulibaly.
Diego Simeone had stints in Serie A as a player with Pisa, Inter Milan and Lazio, helping the latter to the Serie A title in 2000.
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