The 53-year-old former interim Chelsea manager is keen to begin his new role as soon as possible while Marek Hamsik says he wants to stay at Stadio San Paolo
The former Inter coach was named as Walter Mazzarri's successor on Monday, after being released from his contract at Chelsea.
Speaking via the club's official Twitter, he said: "I have been overwhelmed by the messages I have received from all the fans. I cannot wait to begin work at Napoli."
The Spaniard will be boosted by the news that playmaker Marek Hamsik says he wants to continue at the Partenopei.
"I was 19 when I arrived here," Hamsik told the official Fifa website. "Nobody knew who I was but Napoli didn't hesitate to give me a chance.
"For six seasons Napoli and I have developed together, and we can still climb even higher. I'm very comfortable here and I'd like to continue to grow with the club."
However, Benitez is set to face a tougher task in retaining the services of Edinson Cavani beyond this summer, though the striker's agent recently confirmed the Uruguay international would be happy to remain at Stadio San Paolo should a move abroad fail to materialise.
Napoli finished second in Serie A this season and have qualified for the Champions League.