The reigning Serie A champions will have the option to buy Traore for €25m (£21.4m) at the end of the current campaign.
Should they decide against signing the Ivorian on a permanent basis, the Italian club will have to pay Bournemouth a loan fee.
Traore returns to Italy a year after joining Bournemouth on a loan deal from Sassuolo in January 2023, before he completed a permanent transfer to the Cherries in the summer.
The attacking midfielder has featured in just six competitive games this season, with all three Premier League appearances coming from the bench.
Although he has been on the fringes of the squad following Andoni Iraola's appointment in the summer, Traore has been struggling with illness in recent months.
The 23-year-old spent time in hospital after he contracted malaria whilst on international duty with the Ivory Coast in November.
As a result, Traore was forced to miss the Africa Cup of Nations, which is currently taking place in his home country.
The 23-year-old has become Napoli's second signing of the January window following the arrival of defender Pasquale Mazzochi from Salernitana earlier this month.
Traore is unlikely to be involved in the upcoming Italian Super Cup, but he will be hoping to play some role in Napoli's next league game against Lazio on January 28.
After ending their 33-year wait for the Serie A title last season, Napoli are currently in the middle of a difficult campaign.
They were knocked out of the Coppa Italia by Frosinone in December, while they are currently sat in eighth place and 20 points adrift of Serie A leaders Inter Milan.
Walter Mazzarri's side can at least look forward to a Champions League last-16 tie against Barcelona with the first leg set to take place on February 21.
As for Bournemouth, Traore is the second player to leave on loan in just a matter of days after Joe Rothwell recently completed a temporary move to Championship side Southampton.