“He gets things done because of his passion, his competitiveness as a legislator and his persistence,” Mr. Schumer said. “So both sides of the aisle respect and trust Lamar.”
Mr. Alexander made a surprise decision in 2012 to leave the Senate Republican leadership because of a desire to focus more on legislating than on political messaging.
With two years remaining as chairman of the Senate Health, Education, Labor and Pensions Committee, Mr. Alexander said he hoped to devote more time to lowering the overall cost of health care as a way to make insurance coverage more affordable.
He is the first senator to announce his plans for 2020, a presidential election year when control of the Senate will again be up for grabs. His departure comes after Senator Bob Corker, the other Tennessee Republican, decided not to seek re-election this year, meaning the state will lose senior members and committee chairmen in consecutive election cycles.
In recent years, old-guard senators like Mr. Alexander have given way to brasher, more partisan lawmakers, many from the House. Representative Marsha Blackburn, a fellow Republican from Tennessee, will take Mr. Corker’s seat in January, an example of the changing of the guard. Immediately after Mr. Alexander’s announcement, the conservative Club for Growth called on Mark Green, a conservative state legislator newly elected to the House, to seek the open seat.
Mr. Alexander said the state had many possible replacements, but he singled out Gov. Bill Haslam, a Republican, as a formidable candidate, should he choose to run. “We have a barn full of good candidates here,” he said.
Mr. Haslam said he was considering running for the seat.
The senator said his decision was not influenced by any worry about a primary challenge from the right, noting that he had developed a good relationship with President Trump, “though our styles are completely different.” Mr. Alexander said he called Mr. Trump on Sunday night and that before he could break the retirement news, the president said, “Let’s talk about you serving another 20 years.”