The president ordered federal aid for three of the worst affected counties following a request by Governor Earl Ray Tomblin.
West Virginia residents will now receive grants for temporary housing and repairs.
More than 30,000 homes and businesses are without power.
Heavy rain on June 23 turned rivers and streams into torrents, cutting off several towns.
The floods are the worst in a century in some areas and hundreds of people have had to be rescued.
President Barack Obama “ordered federal aid to supplement state and local recovery efforts in the area affected by severe storms, flooding, landslides and mudslides”, a White House statement said.
Governor Tomblin said the federal help included medical support and housing to Kanawha, Greenbrier and Nicholas counties.
Officials were still assessing the damage in other areas and additional requests for aid could follow, the governor added.
West Virginia received a quarter of its annual rainfall in a single day, the US National Weather Service said.
A storm system dumped up to 10 inches of rain on parts of the state, causing rivers and streams to overflow.
More than 100 homes were destroyed, some of them torn from their foundations and carried away, and an estimated 32,000 residences were still without power.
Teams removed people from upper-floor windows, tops of trees and cars.
According to officials, among those rescued were a 97-year-old woman and a family of five, including an infant.
About 500 people were trapped in a shopping centre as crews scrambled to build a new gravel road to reach them.
Meanwhile, rescue teams continued to try to reach others stranded in devastated areas.
States of emergency have been declared in 44 of the state’s 55 counties, and up to 500 soldiers have been authorized to assist in the rescue operations.
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