And Mr. Trump used a speech in Salt Lake City to say that he hoped Mr. Hatch would “continue to serve your state and your country in the Senate for a very long time to come.”
Then on Dec. 20, at a White House event celebrating passage of the comprehensive tax cut that Mr. Hatch helped write, the president pulled him aside to again ask him to run.
The senator lauded Mr. Trump at the event, calling him “one heck of a leader.”
“We are going to make this the greatest presidency we have seen, not only in generations, but maybe ever,” Mr. Hatch said.
But the presidential intervention failed. Mr. Hatch decided to retire after discussing the matter with his family over the holidays.
That clears the way for the political resurrection of Mr. Romney, the former Massachusetts governor and 2012 Republican presidential nominee who is now a Utah resident and is popular in the Mormon-heavy state, where he ran the 2002 Winter Olympics. Mr. Romney has told associates he would likely run if Mr. Hatch retires.
“He’d be a very difficult candidate to beat in Utah,” said Michael O. Leavitt, a former Republican governor of Utah.
Mr. Romney repeatedly assailed Mr. Trump during the 2016 campaign, calling him “a fraud,” and Mr. Trump returned the favor, stating that Mr. Romney “choked like a dog” in the 2012 race. The two had something of a rapprochement after the election when Mr. Romney was briefly considered as secretary of state, but after Mr. Trump’s equivocating statements that followed the racist and anti-Semitic violence in Charlottesville, Va., last summer, Mr. Romney regained his critical voice.
“Whether he intended to or not, what he communicated caused racists to rejoice, minorities to weep, and the vast heart of America to mourn,” Mr. Romney wrote of Mr. Trump’s statements. “His apologists strain to explain that he didn’t mean what we heard. But what we heard is now the reality.”
When it comes to Mr. Trump, Mr. Leavitt said, Mr. Romney has “not been reluctant to speak his mind, and I can’t imagine he would change in the Senate.”
In a statement he posted on Facebook on Tuesday, Mr. Romney made no mention of his intentions; he only saluted Mr. Hatch.
“As Chairman of the Senate Finance and Judiciary Committees and as the longest-serving Republican Senator in U.S. history, Senator Hatch has represented the interests of Utah with distinction and honor,” he said.
By Tuesday evening, Mr. Romney had updated his Twitter profile to change his location to Holladay, Utah, from Massachusetts.
Mr. Romney intends to make his intentions known in a matter of weeks, according to an adviser who spoke on the condition of anonymity. His senior campaign team will include Mr. Zwick; Matt Waldrip, who had been running Mr. Romney’s annual policy retreats; and his former chief of staff, Beth Myers.
Mr. Zwick did not confirm Mr. Romney would enter the race, but said that “of all the people who can run, Mitt will represent and honor the legacy of Senator Hatch more than anybody.”
Mr. Hatch, who briefly ran for president in 2000, amassed a distinguished record over his four decades in Washington and became a fixture in a Senate once noted for its bipartisanship. While considered an institution in his home state, Mr. Hatch was facing harsh poll numbers in Utah, where 75 percent of voters indicated in a survey last fall that they did not want him to run again.
Mr. Hatch’s decision comes just weeks after Mr. Trump signed the tax overhaul into law, a measure that the senator helped shepherd as chairman of the Finance Committee. The bill represented something of a capstone to Mr. Hatch’s career, and Senator Mitch McConnell, Republican of Kentucky and the majority leader, even deemed it as such last month in what was seen as a subtle effort to usher his colleague to the exit.
Mr. Romney was unaware of Mr. Hatch’s decision and of late had been operating under the assumption that the senator would run again, not even bringing up the possibility of a campaign while skiing Monday with friends in Utah.
That is in part because Mr. Hatch had privately told Mr. Romney he was not sure he was ready to leave a seat he has held since 1977, and White House officials did all they could to nudge him into another campaign.
The president has had Mr. Romney on his mind. Over golf last year, Mr. Trump asked Senator Lindsey Graham, Republican of South Carolina, what he thought of the former Republican nominee. (Mr. Graham said he praised Mr. Romney and predicted he would be a solid senator.)
As the president prodded Mr. Hatch to stay, voices in his home state were urging him to go. On Christmas Day, The Salt Lake Tribune named the senator “Utahn of the Year,” but not for flattering reasons.
“It would be good for Utah if Hatch, having finally caught the Great White Whale of tax reform, were to call it a career. If he doesn’t, the voters should end it for him,” the editorial concluded.
In announcing his retirement, Mr. Hatch joined an exodus of Republican heavyweights in what promises to be a difficult election season. Also on Tuesday, Representative Bill Shuster of Pennsylvania, the chairman of the House Transportation Committee, disclosed that he planned to retire at the year’s end. Mr. Shuster, 56, was facing a possible primary election challenge from the right and said his decision would allow him to focus exclusively on trying to steer major infrastructure legislation, a long-sought bipartisan priority, into law.
Other retiring House chairmen include Robert W. Goodlatte of Virginia, of the Judiciary Committee; Jeb Hensarling of Texas, of the Financial Services Committee; and Lamar Smith of Texas of the Committee on Science, Space and Technology.
In all, 29 House Republicans have resigned, announced they will retire or run for another office, compared to 16 Democrats. Mr. Hatch joined Senators Bob Corker of Tennessee and Jeff Flake of Arizona, both Republicans, in announcing an end to his Senate career.
Mr. Hatch defeated a Democrat 42 years ago this November, arguing that the incumbent had stayed in Washington too long, and became one of the country’s most prominent senators for a generation. While he usually voted a conservative line, he also developed close relationships with his Democratic colleagues, most famously with Senator Edward M. Kennedy of Massachusetts. In the 1990s, the two collaborated on what became a landmark health care plan, the State Children’s Health Insurance Program, and Mr. Hatch even wrote a love song for Mr. Kennedy and his wife, Victoria, called “Souls Along The Way.”
“Orrin’s long list of accomplishments means he will depart as one of the most productive members ever to serve in this body,” Mr. McConnell said in a statement.