HONOLULU, Hawaii—On Christmas Eve 2014, Malaysian Prime Minister Najib Razak stepped onto Hawaii’s 18-hole Kaneohe Klipper course for a round of golf diplomacy with U.S. President Barack Obama.

Off the fairways, another side of Mr. Najib’s time in office was on display. Two days earlier, the prime minister’s credit card was charged $130,625 to Chanel in Honolulu, according to Malaysian investigation documents. A person who works at a Chanel store in the upscale Ala Moana Center recalls Mr. Najib’s wife shopping there just before Christmas.

The credit card was paid from one of several private bank accounts owned by Mr. Najib that global investigators believe received hundreds of millions of dollars diverted from a government investment fund set up by the prime minister in 2009. The fund, 1Malaysia Development Bhd., or 1MDB, today is at the center of corruption probes by authorities in Malaysia and at least five other nations.

The Malaysian investigation documents, viewed by The Wall Street Journal, contain bank-transfer information that provides the most complete picture to date of the money that flowed through the prime minister’s accounts over a five-year period, the majority of it, investigators say, originating from 1MDB.

They show for the first time how some of the money in Mr. Najib’s accounts allegedly was used for personal expenses. That included $15 million in spending on clothes, jewelry and a car, according to the bank-transfer information, involving stores in the U.S., Malaysia, Italy and elsewhere.