Tokyo gained 0.83%, or 127.19 points, to 15,449.79 and Seoul added 0.88%, or 18.01 points, to 2,071.14.
Sydney rose 0.66%, or 36.7 points, to 5,623.8.
Global mining giant BHP posted a 23.2% jump in annual net profit and said it would create a new independent company by spinning off non-core assets to reduce costs and boost productivity.
Shares in BHP closed 1.35% higher ahead of the announcement.
Hong Kong climbed 0.67%, or 167.49 points, to 25,122.95 and Shanghai ended up 0.26%, or 5.86 points, at 2,245.33
The gains came after US stocks rebounded on Monday from last week's Ukraine-linked setback, with the Dow surging and the Nasdaq reaching a 14-year high.
The Dow Jones Industrial Average finished up 1.06% at 16,838.74 while the broad-based S&P 500 added 0.85% to 1,971.74.
The Dow had led a sell-off on Friday as news that Ukrainian artillery had destroyed part of a Russian military column spooked investors.
But Russia on Monday said that "certain progress" had been made during a marathon meeting in Berlin between the two countries' foreign ministers and their counterparts from Germany and France.
The tech-rich Nasdaq Composite gained 0.97% to 4,508.31 — its highest level since March 31, 2000, when the market was on the cusp of a nearly 4,000-point crash as the tech bubble burst.
In forex markets, the dollar was at 102.62 yen in afternoon Asian trade, up from 102.57 yen in New York late on Monday and 102.32 yen in Tokyo earlier on Monday.
The greenback is expected to bounce in volatile forex trading this week, ahead of a speech on Friday by US Federal Reserve chief Janet Yellen at the central bank's annual economic policy symposium. Investors will be looking for any hint of a change to the Fed's interest rate plans.
Last month, Yellen told Congress the Fed would hold its near-zero interest rate policy until the US economy strengthens, but may raise rates if the jobs market keeps improving.
Later Tuesday, investors were looking to US inflation data for July to get a snapshot of the state of the world's number one economy.
The euro bought $1.3351 and 137.04 yen against $1.3363 and 137.05 yen in US trade.
In oil markets, US benchmark West Texas Intermediate for September delivery rose 38 cents to $96.79 while Brent crude for October was up 23 cents to $101.83.
Gold traded at $1,300.30 an ounce at 1050 GMT compared to $1,302.22 an ounce late Monday.
In other markets, Singapore rose 0.11%, or 3.65 points, to 3,316.43. Agribusiness company Wilmar International was down 0.32% at S$3.16 while real estate developer Capitaland advanced 2.13% to S$3.36.
Kuala Lumpur gained 0.56%, or 10.41 points, to 1,872.16. Utility giant Tenaga Nasional added 0.8% to 12.40 ringgit, while Public Bank rose 0.5% to 19.34. UMW Holdings fell 0.5% to 12.30 ringgit.
Bangkok added 0.03%, or 0.49 points, to 1,542.85. Food production company Charoen Pokphand Foods rose 3.45% to 30.00 baht, while residential developer Pruksa Real Estate gained 2.16% to 35.50 baht.
Jakarta ended up 0.16%, or 8.42 points, at 5,165.17. Palm oil firm Astra Agro Lestari gained 1.82% to 26,550 rupiah, while food manufacturer Indofood Sukses Makmur slipped 1.75% to 7,000 rupiah.
Wellington rose 0.85%, or 43.09 points, to 5,114.21. Air New Zealand was up 2.44% at NZ$2.095 and Fletcher Building gained 0.44% to NZ$9.09.
Taipei jumped 1.12%, or 102.47 points, to 9,243.78. Taiwan Semiconductor Manufacturing Co was 0.81 percent higher at T$124.0 while leading chip design house MediaTek gained 2% to T$510.0.
Manila climbed 0.79%, or 55.17 points, to 7,082.75. Top-traded Philippine Long Distance Telephone Co rose 0.43% to 3,250 points while Ayala Land Inc added 1.69% to 33.15 pesos.
Mumbai rose 0.11%, or 29.71 points, to 26,420.67 points. In the session, the 30-stock benchmark index briefly touched a new high of 26,530.67 points. Muthoot Finance soared 9.65% to 194.95 rupees, while Berger Paints climbed 9.13% to 340.00 rupees.