The Argentina striker, who was a reported target of Chelsea in the winter transfer market, is Napoli's top scorer this season with 12 goals in 22 Serie A games.
"This is an important time for me and for my career. I've been playing at the highest level for eight years and I feel physically well, and there's a great atmosphere in Naples."
The 26-year-old turned down an offer from Juventus shortly before joining Napoli from Real Madrid in a £34.5m transfer deal last summer.
"Juve executives spoke to my family but I already had an offer from Napoli," Higuain said. "I also received a phone call from (Napoli coach Rafa) Benitez that convinced me in no time of Napoli's project. After speaking to my father, I decided to turn down the other offers and go for Napoli."
Napoli are third in Serie A and hold the last UEFA Champions League qualifying spot. They are also alive in the UEFA Europa League and the Coppa Italia.
"We hope we can win a title this season," Higuain said. "We believe it is possible.
"There are three titles up for grabs and although we know it will be very difficult, we are very determined to surprise everyone."