Across the state, homes were washed away, streets became rivers and water on highways reached signs 16ft overhead.
Among the dead was a woman who got out of her car in high water trying to reach safety.
Another person died in a fire at their home.
Desperate families clambered onto roofs to wait for helicopter rescue as water poured through doors and windows.
Harvey made landfall on Friday at Corpus Christi, on the Gulf coast, as a Category 4 storm with 130mph winds – the most powerful since Hurricane Katrina in 2005.
The worst-affected town is Rockport, which is in ruins.
By the time Harvey reached Houston, a city of 2.3 million people, on Saturday it was downgraded to a Tropical Storm but was still dumping 40 inches of rain.
Amid apocalyptic scenes people walked through waist-high water carrying children and belongings on their backs as meteorologists said the ‘catastrophic’ rainfall would continue for days.
Houston Mayor Sylvester Turner said 2,000 had been rescued but the 911 system was overloaded.
He told residents: “We will get to you and we will get through this.”
US President Donald Trump is expected to visit Texas this week.