"But every good fighter knows when to hang up the gloves." said Hatch in the video.
During an event last month at the Utah Capitol where Trump celebrated the administration's decision to shrink the Bears Ears and Grand Staircase-Escalante national monuments, Trump called Hatch "a true fighter" and said he hoped the Republican would continue to serve "in the Senate for a very long time to come".
Mitt Romney, former MA governor and GOP presidential nominee, is expected to run for Hatch's seat.
Former Republican presidential nominee Mitt Romney, a vocal critic of President Donald Trump, could be poised for a political comeback.
I join the people of Utah in thanking my friend, Senator Orrin Hatch for his more than forty years of service to our great state and nation.
Romney did not have an immediate public reaction to Hatch's announcement.
The powerful Senate Finance Committee chairman played a significant role in helping Republicans pass a major tax overhaul before Christmas.
At a rally for Alabama Senate candidate Roy Moore, Bannon called Romney, the GOP's 2012 presidential nominee, a draft dodger who "hid behind" his religion.More news: Millions across the World celebrate as 2018 rolls in
Mr Romney has been quiet about his plans and views of late.
Hatch, 83, was first elected in 1976 and had spent months publicly deliberating about whether to stand again for reelection in November.
The senator returned the favor at the White House when Mr. Trump signed the tax measure, calling him "one heck of a leader". Mr. Romney has told associates he would likely run if Mr. Hatch retires.
That dynamic sparked a recent lobbying effort by the White House to encourage Hatch to seek another term in office.
"Senator Hatch has represented the interests of Utah with distinction and honor", Romney wrote. Sherrod Brown of OH after Brown said Republican tax cuts were aimed at helping the rich. Should they decide to run, their presence might be a welcome bit of nostalgia to GOP voters tired by Trump's presidency; but they could also provide an unwelcome flashback.
Bloomberg News reported in October that Bannon was planning to play in nearly every Republican Senate primary contest, anyway, but a couple of the Breitbart News chief's would-be targets - Sen.
In 2000, Hatch sought the Republican nomination for president, saying he had more experience in Washington than his opponents and insisting he could work with Democrats.