The release of the Terrex vehicles closes the curtain on a diplomatic row that also involved China, which has sovereignty over Hong Kong and considers Taiwan a renegade island awaiting reunification.
"Terrexes left Hong Kong port this morning at 0415hrs. Next stop, home," Defence Minister Ng Eng Hen said in a Facebook post.
Ng had said on Wednesday that the journey would take a week.
Hong Kong customs authorities had impounded the vehicles in November while they were being shipped home following exercises in Taiwan, where land-starved Singapore has for decades trained its troops.
Ties between China and Singapore were already strained over the city-state's perceived support for Southeast Asian nations disputing Beijing's extensive territorial claims in the South China Sea.
Hong Kong is semi-autonomous after being handed back by Britain to China in 1997. But Beijing controls foreign affairs issues and there are increasing fears over its interference in other matters.
Disclaimer: No Business Standard Journalist was involved in creation of this content