Hong Kong rallied 1.69%, or 394.97 points, to close at 23,782.11 — its highest level since December —and Shanghai rose 1.02%, or 21.00 points, to 2,075.48.
Tokyo closed up 0.84%, or 127.57 points, at 15,343.28, Seoul ended 0.52% higher, adding 10.43 points to 2,028.93, and Sydney ended up 0.06%, or 3.4 points, at 5,543.3.
Taipei rose 0.62%, or 58.39 points, to 9,499.36, and Manila ended marginally lower, dipping 4.94 points to 6,869.94.
The downing of the Malaysia Airlines jet last Thursday in Ukraine fanned fears that a regional crisis could become an international one, with Western governments saying it was shot down by pro-Russian separatists.
Those tensions eased on Tuesday after it emerged the rebels had given the plane's two black boxes to Malaysian officials.
They also announced a ceasefire in an area around the crash site to provide safe access for an international investigation.
And they allowed a train carrying the remains of 280 of the people killed in the disaster to leave the region.
The improved sentiment filtered through to currency markets, with the yen easing as investors grow more confident in higher-risk assets. The Japanese unit is considered a safe haven in times of uncertainty.
In the afternoon the dollar was worth 101.50 yen compared with 101.38 yen in New York, while the euro rose to 137.15 yen from 137.10 yen.
The single currency bought $1.3521 against $1.3523.