Wall Street and bourses across Europe have been recovering some of the ground since the UK voted last week to leave the European Union.
In Japan, the benchmark Nikkei 225 share index finished 1.6% higher at 15,566.83.
Shares in carmaker Toyota rose by more than 2% despite fresh recalls over faulty airbags.
Other markets across Asia also saw gains, despite the continued uncertainty in the wake of the UK's referendum vote.
Investors are hoping that central banks will step in with more stimulus measures should the global economy weaken.
Hong Kong's Hang Seng closed 1.3% higher at 20,436.12 while the mainland benchmark Shanghai Composite finished up 0.65% at 2,931.59.
In Australia, the ASX/200 index also closed higher, up 0.8% at 5,142.40.  Shares in commodity giants Rio Tinto and BHP Billiton were both up by almost 2%.
In South Korea, the Kospi share index finished 1% higher at 1,956.36.
Asian stock markets have recorded more gains, continuing the positive lead set by the US and Europe on Tuesday.