The law also prohibits the cities from calling themselves "sanctuary cities".
The governor called out Travis County Sheriff Sally Hernandez, who he said instituted "sanctuary city" policies that limited cooperation between officers in her jurisdiction and immigration authorities.
The governor signed the controversial bill at 6:30 p.m. using Facebook live on the official page of the Texas governor.
Now, law enforcement agencies across the state are required to honor U.S. Immigration and Customs enforcement detainers.
Sheriffs, police chiefs or constables who don't comply with I.C.E. requests to keep someone in custody could face jail time. The new law goes into effect September 1.
Reaction to the signing spread swiftly in Texas and beyond.
The law has previously drawn criticism from leaders in Bexar County including San Antonio Police Chief William McManus.
Neymar Facing Prison Sentence?
The transfer figure originally published by Barcelona was €57.1m (£48.4m) with €40m euros (£33.9m) of that given to his family. Barca have won back-to-back Spanish league and Cup doubles with the trio and won the Champions League in 2015.
"Quite frankly I think it was a cowardly way to do it", State Rep. César Blanco, a Democrat representing El Paso, said in an interview with The Washington Post.
"The voters should at least know the minimum of what newly minted U.S. citizens are required to know", unusual said, "In my opinion, its just a matter of opinion, but I think it's a good effort to introduce this requirement for high schools". "This for his primary voters, not for mainstream Texas". "They expected him to be there and to be more public so people could raise their voices".
Dozens of protesters gathered outside the Governor's Mansion in Austin to condemn the bills approval Sunday evening. Immigrant rights activists shouted "here to stay" and held up a banner with a words, "Abbott is a racist".
Protests over the bill have been intense for months. "This bill that will terrorize communities". By signing it on Sunday, he avoided any showdown.
"It's ironic that he does it on a Sunday when families are together and this legislation is only going to tear families apart", Blanco said. He said Texas residents expect lawmakers to "keep us safe" and said similar laws have already been tested in federal court, where opponents have said the bill likely will be immediately challenged.
Thomas Saenz, president of the Mexican American Legal Defense and Education Fund, said millions in the nation's second most populous state will now be subjected to racial profiling and may be less willing to cooperate with police investigations. With a stroke of his pen, Governor Abbott has undermined democracy and voters' right to choose their elected officials, alienated almost half the state population now subject to widespread racial profiling, severely undermined public safety by triggering widespread non-cooperation with police investigations of real crime, subjected Texas businesses tied to trade or tourism to incalculable losses, and exposed the state's taxpayers to substantial costs related to multiple statewide and local challenges to this inhumane law.