It aims to wean the kingdom off oil, which remains its main revenue source even though global prices have fallen by around half since 2014.
Vision 2030 and the National Transformation Programme, which sets targets for implementing it, seek to boost non-oil revenues and employ more Saudis.
In line with the Vision, ministers on Monday approved rules for foreign companies to invest in the wholesale and retail trade sector with 100 percent ownership, up from 75 percent.
Dow said the trading licence advances its ability to deliver products in the areas of sustainable development, energy efficiency, oil and gas, alternative energy and water.
After Prince Mohammed met Treasury Secretary Jack Lew and other top US economic policymakers on Wednesday, the White House "underscored the United States' desire to be a key partner in helping Saudi Arabia implement its ambitious economic reform programme."
Dow calls itself Saudi Arabia's largest foreign investor.
Its stakes include Sadara Chemical Co, a joint venture with Saudi oil giant Aramco.
Commerce and Investment Minister Majed al-Qasabi, in the United States with Prince Mohammed, said on Tuesday that the new ownership rules "take us a step further" towards the Vision's goal of making Saudi Arabia an investment powerhouse.
Investors will now have flexibility to structure their company optimally to benefit from the Saudi market, the Saudi Arabian General Investment Authority said.
"They may seek 100 percent ownership or operate through a joint venture," it said.