By ALAN RAPPEPORT and MAGGIE HABERMAN

Sarah Palin, the former Alaska governor and 2008 vice-presidential nominee who became a Tea Party sensation and a favorite of grass-roots conservatives, endorsed Donald J. Trump in Iowa on Tuesday, providing Mr. Trump with a potentially significant boost just 13 days before the state’s caucuses.

“Are you ready for the leader to make America great again?” Ms. Palin said with Mr. Trump by her side at a rally at Iowa State University. “Are you ready to stump for Trump? I’m here to support the next president of the United States – Donald Trump.”

Her support is the highest-profile backing for a Republican contender so far. It came the same day that Iowa’s Republican governor, Terry Branstad, said he hopes that Senator Ted Cruz will be defeated in Iowa, where the Feb. 1 caucuses are a must-win for the Texas senator, who is running neck-and-neck with Mr. Trump in state polls.

The endorsement came as Mr. Trump was bearing down in the state, holding multiple campaign events and raising expectations about his performance in the nation’s first nominating contest.

As Mrs. Palin announced her backing, Mr. Trump stood wearing a satisfied smile as she scolded mainstream Republicans as sell-outs and praised how Mr. Trump had shaken up the party.

“He’s been going rogue left and right,” Ms. Palin said of Mr. Trump, using one of her signature phrases. “That’s why he’s doing so well. He’s been able to tear the veil off of this idea of the system.“

In Iowa, where Ms. Palin spent years developing a network of supporters, the endorsement could be especially helpful. Mr. Trump has faced questions about whether his campaign’s organizing muscle can draw the voters to match his poll numbers come caucus night.

”Over the years Palin has actually cultivated a number of relationships in Iowa,” said Craig Robinson, the former political director of the Republican Party of Iowa and publisher of the website The Iowa Republican. ”There are the Tea Party activists who still think she’s great and a breath of fresh air, but she also did a good job of courting Republican donors in the state,” he added.

Other conservatives said that Ms. Palin serves as a particularly effective shield against Mr. Cruz, who has assidously courted Iowa’s evangelical voters.

“Palin’s brand among evangelicals is as gold as the faucets in Trump tower,” said Ralph Reed, the chairman of the Faith and Freedom Coalition.

“Endorsements alone don’t guarantee victory, but Palin’s embrace of Trump may turn the fight over the evangelical vote into a war for the soul of the party,” he said.

Mrs. Palin could amplify the news media-circus aspects of Mr. Trump’s candidacy: Like him, she is a reality-TV star accustomed to playing to the cameras and often accused of emphasizing flash over substance.

What’s more, while Mr. Trump has already shown the ability to garner wall-to-wall cable-news coverage, Mrs. Palin’s active involvement in his campaign could help him deprive Mr. Cruz of vital attention in the homestretch to the Feb. 1 caucuses.

As rumors circulted that the endorsement was about to happen, Mr. Cruz offered praise for his former close politcal ally after an aide to the senator mocked the pending endorsement earlier Tuesday. “I love Sarah Palin,” the senator told reporters in New Hampshire. “Sarah Palin is fantastic. Without her friendship and support, I wouldn’t be in the Senate today. So regardless of what Sarah decides to do in 2016, I will always remain a big, big fan of Sarah Palin.”

As word of Ms. Palin’s endorsement trickled through the Hansen Agricultural Student Learning Center at Iowa State University, the reaction from supporters of Mr. Trump who braved snow and frigid temperatures to see the candidate was mixed. Backers of Mr. Trump filled a warehouse-style building with a dirt floor that is sometimes used for tractor shows, but most said that it was the candidate that they cared about most, not his new endorsement.

“I’m not here to see her,” said Rich Hoffmann, 41, of Ankeny. “Some people it will matter to, but it doesn’t to me.”

Mrs. Palin and Mr. Trump are not strangers. The two shared pizza along with Mr. Trump’s wife, Melania, in June 2011, when Mrs. Palin was considering a presidential run of her own and was making a bus tour around the country. (Mr. Trump was mocked at the time for using a knife and fork on his slice.)