Oil Search, whose assets are mostly based in the Pacific island nation, said it was reviewing the bid that will see Woodside offer one share for every four Oil Search shares.
Oil Search was valued at about Aus$11.6 billion, a 14 percent premium to its closing share price of Aus$6.73 on Monday when Woodside closed at Aus$30.58.
The proposal is subject to satisfactory due diligence and regulatory approvals, as well as support from Oil Search's major shareholder, the PNG government.
Oil Search's share price surged 17.38 percent to close at Aus$7.90, while stocks in Woodside slipped 3.01 percent to end the day's trade at Aus$29.66.
The announcement buoyed energy stocks on the benchmark S&P/ASX200 index, with Santos closing 5.25 percent higher and AGL rising 3.68 percent.
Oil Search stressed that shareholders were "entitled to an offer which adequately reflects this value potential", pointing to its share in the massive US$19 billion PNG liquefied natural gas project -- the largest development ever undertaken in the Pacific country.
The company said along with its other low-cost producing assets it was well-placed to capitalise from a recovery in the oil price, which has roughly halved in a year.
Woodside last month reported a 39 percent drop in net profit to US$679 million in the six months to June 30, saying the decline was due to falling commodity prices.
Oil Search said it recorded a net profit of US$227.5 million for the same period, a 49 percent increase from the prior year, as higher sales volumes partly offset weaker oil and gas prices.