"We are witnessing a great awakening," Cruz told supporters at a Houston hotel victory celebration.
"Millions of Texans, millions of Americans, are rising up to reclaim our country, defend liberty and restore the Constitution," he said. "We are rising up to take our country back."
Cruz, 41 -- a Cuban-American Harvard-trained lawyer who has argued cases before the Supreme Court but had never before run for office -- defeated Republican Texas Lt. Gov. David Dewhurst, 56 percent to 44 percent, with virtually all precincts reporting.
Dewhurst was favored by the Republican Party establishment, including Texas Gov. Rick Perry.
Both men sought Republican support for the Senate seat being vacated by Kay Bailey Hutchison, the most senior female GOP senator.
No Democrat has won a statewide Texas vote since 1994.
In his speech, Cruz praised God -- "To Him be the glory" -- and thanked a long list that included conservative radio and TV hosts Glenn Beck and Sean Hannity, libertarian-leaning presidential hopeful and U.S. Rep. Ron Paul, R-Texas, and his son, Sen. Rand Paul, R-Ky., Martin Luther King Jr. and even Dewhurst.
"I salute Mr. Dewhurst for his many years in the Air Force, in the CIA and as lieutenant governor," Cruz said.
Dewhurst, 66, a wealthy rancher and powerful GOP figure who spent freely from his vast personal fortune, told glum supporters in a neighboring hotel, "We got beat up a little, but we never gave up."
He said he was not accustomed to losing an election.
"We will never stop fighting for our beloved Texas," Dewhurst said.
The Houston Chronicle said his voice cracked as he spoke.
"We will never stop fighting for our conservative principles," he said. "We will never stop fighting President Barack Obama and his liberal agenda."
Dewhurst will continue as lieutenant governor.
Cruz's win will go down as one of the Tea Party's biggest wins of the year, alongside that of Indiana state Treasurer Richard Mourdock's primary win over Sen. Richard Lugar, R-Ind., in May, The Hill said.
It also echoes Cuban-American Marco Rubio's Senate victory in 2010 over Republican Florida Gov. Charlie Crist, The New York Times said.
2014: The Year in Music [PHOTOS]