AUSTIN, Texas—Texas, headquarters of America’s oil industry, is about to stake a fortune on wind power.

In what experts say is the biggest investment in the clean and renewable energy in U.S. history, utility officials in the Lone Star State gave preliminary approval Thursday to a $4.9 billion plan to build new transmission lines to carry wind-generated electricity from gusty West Texas to urban areas like Dallas.

Texas is already the national leader in wind power, generating about 5,000 megawatts. But wind-energy advocates say the lack of transmission lines has kept a lot of that power from being put to use and has hindered the building of more turbines.

Supporters say Thursday’s 2-1 vote by the Texas Public Utility Commission is critical to getting that energy to more people.

Most of Texas’ wind-energy production is in petroleum-producing West Texas, where nearly 4,000 wind turbines tower over oil pump jacks and capture the breeze that blows across the flat and largely barren landscape. The new plan would not directly build a slew of new turbines, but would add transmission lines capable of moving about 18,000 megawatts. One expert said that is enough to power more than 4 million Texas homes.

Supporters predict the plan will spur new wind power projects, create jobs, reduce pollution and lower energy costs. Texans pay some of the highest electric rates in the country, in part because of congested transmission lines.

Texas electric customers will bear the cost of construction over the next several years, paying about $3 or $4 more per month on their bills, according to Tom Smith, state director of the consumer group Public Citizen. But he predicted that increase would easily be offset by lower energy prices.