MOSCOW — Exxon Mobil won a coveted prize in the global petroleum industry Tuesday with an agreement to explore for oil in a Russian portion of the Arctic Ocean that is being opened for drilling even as Alaskan waters remain mostly off limits.

The agreement seemed to supersede a similar but failed deal that Russia’s state oil company, Rosneft, reached with the British oil giant BP this year — with a few striking differences.

Where BP had planned to swap stock, Exxon, which is based in Texas, agreed to give Rosneft assets elsewhere in the world, including some that Exxon owns in the deepwater zones of the Gulf of Mexico and on land in Texas.

In announcing the arrangement at a surprise signing in the Russian resort town of Sochi, Prime Minister Vladimir V. Putin described a sweeping global alliance — and a potentially vast investment by Exxon in the Russian Arctic.