The Serie A club were deducted two points by the Italian Football Federation (FIGC) on 18 December for being "objectively responsible" for the actions of former goalkeeper Matteo Gianello, who tried to fix a match with Sampdoria in 2010.
The six-month bans issued to defenders Paolo Cannavaro and Gianluca Grava for failing to report an approach from Gianello have also been reversed by the FIGC's appeal court.
The duo are now available for selection against Fiorentina on Sunday, and Cannavaro said: "It's an immense feeling of joy. It was a terrible month, hell. Now this is a release.
"I was in a really bad way. I won't be able to forget what I went through this month. I thank all those who were close to me. I want to thank the club for all that they did, the coach and my team-mates that have consoled me every day."
Napoli will now climb to second in the Italian top-flight above Lazio, leaving them three points behind leaders Juventus.
A statement published on the FIGC's official website also confirmed the initial fine of 70,000 euros issued to the club has also been reduced.
"The two penalty points issued to Napoli have been revoked, but the club will pay a fine of 50,000 euros," it read.
"There are acquittals for Paolo Cannavaro and Gianluca Grava, while the disqualification of Matteo Gianello has been reduced from three years and three months to one year and nine months.
"These are the decisions of the Federal Court of Justice following appeals against the judgments made by the Naples branch of the disciplinary committee on match-fixing."
Quoted in the Gazzetta dello Sport, club lawyer Mattia Grassani said: "It's a sensational victory and a really important result.
"Above all, justice has been done and what was unjustly taken from Napoli and its fans has been returned.
"It was a joy to inform president (Aurelio) De Laurentiis after I received the official report from the appeal court.
"This decision closes a really sad story for which Napoli and its players paid a very high price regardless."