The length of the 25-year-old's contract is yet to be confirmed by the club, but he is said to have signed until 2024 and becomes Napoli's second signing of the month following Diego Demme's switch from RB Leipzig.
Napoli are reported to have paid an initial €20m, with another €4m in variables and clauses.
Lobotka joined Celta in 2017 from Danish side Nordsjaelland and the Slovakia international quickly established himself in Juan Carlos Unzue's team, playing every match in the 2017-2018 campaign and starting 34 of them.
He remained a key player until his departure, often earning rave reviews with his enterprising blend of technical quality and combativeness.
The last Slovakian player to represent Napoli was Marek Hamsik, who went on to become a club icon after spending almost 12 years in Naples until last February.
Lobotka leaves a significant hole to fill for Celta, who are languishing just above the relegation zone in LaLiga, with goal difference the only metric keeping them out of the bottom three.