It will be the longest tour of Asia by a US president in 25 years, reports the BBC.
The trip comes at a time of heightened tensions with North Korea over its nuclear programme and missile tests.
Trump is expected to show a united front with South Korea and Japan while pressing China to take a stronger line with Pyongyang.
On Friday, Trump flew first to the US state of Hawaii where he took part in a briefing at the US Pacific Command. He will also visit the USS Arizona Memorial at Pearl Harbor – the scene of the 1941 Japanese attack that drew the US into World War Two.
From Hawaii, he and First Lady Melania Trump will head to Japan (Sunday) and then on South Korea (November 7).
Trump will visit Camp Humphreys, a US military complex south of Seoul but would not go to the heavily fortified demilitarized zone (DMZ) on the border between the South and North.
After South Korea, Trump will arrive in China on November 8 where he will participate in a series of events with his counterpart Xi Jinping, the BBC reported.
In Vietnam (November 10-11), Trump will attend the Asia-Pacific Economic Co-operation summit in Danang and make a state visit to Hanoi.
His final engagement will be a summit of South-East Asian nations in the Philippine capital, Manila (November 12-13).
The last time a US president made such a marathon trip to Asia was when George.H.W. Bush visited the region in late 1991 and early 1992.