The warplanes are part of an $8 billion deal for 66 F-16Vs approved during US President Donald Trump's first term and scheduled for delivery this year.
China claims Taiwan is part of its territory and has threatened to use force to seize it, with Beijing opposing US arms sales to the island.
The two F-16Vs, made by US defence contractor Lockheed Martin, are to touch down at Taiwan's Air Force Base in Taitung, on the island's southeast coast.
The jets had been expected to arrive in early September after making refuelling stops in Hawaii and Guam.
Local media reported that the planes had turned back to Hawaii shortly after taking off for Guam. No official explanation was given.
Dozens of locals, some equipped with binoculars and long-lensed cameras, gathered near the air base's perimeter fence to watch the highly anticipated arrival of the jets.
Kimi Chi, a salesman from the central city of Taichung, had travelled through the night to be able to photograph the aircraft landing in Taitung.
He was philosophical about the delays, saying "good things take time."
"In terms of hardware capabilities, there will definitely be an improvement," the 37-year-old told AFP.
"But what we are actually lacking the most right now is pilots. Of course, I hope the government can provide better additional allowances for these military pilots."
Former Air Force serviceman Eric Chan, 57, marvelled at the improvements made to the F-16 over the past 30 years and said the fighter jets based in Taitung will "play a very important defensive role" against China.
"The threat from the CCP has always been there so we definitely need to strengthen our defence capabilities," Chan told AFP, referring to the Chinese Communist Party.
The United States is Taiwan's most important security backer and biggest arms supplier. But bottlenecks in the US defence industrial base have slowed delivery of critical weapons.
Taiwan's Defence Minister Wellington Koo said previously it would be "challenging" for all the F-16Vs to be delivered this year, despite Lockheed Martin ramping up production.
The arrival of the F-16Vs comes as Taiwan awaits Washington's approval of a separate $14 billion arms package.
Trump has paused the record weapons purchase by Taipei, calling it in May a "very good negotiating chip" in dealings with China, which raised fears that Taiwan's security could be traded away.
