"I am running for the U.S. Senate from the Great State of Arizona, for one unwavering reason: to support the agenda and policies of President Donald Trump in his mission to Make America Great Again," he posted on Twitter.
Arpaio also told supporters in a fundraising email that he filed the paperwork to run in Arizona's Republican primary in late August.
Republican Jeff Flake said in October he would not seek re-election.
"I have a lot to offer. I'm a big supporter of President Trump," Arpaio said in the interview. "I'm going to have to work hard; you don't take anything for granted. But I would not being doing this if I thought that I could not win. I'm not here to get my name in the paper, I get that everyday, anyway."
Arpaio served as sheriff in Maricopa County, which includes Phoenix, for 24 years until he was defeated by a Democrat in 2016, Paul Penzone. Arpaio has called himself "America's toughest sheriff."
While in charge of the jail, he put inmates on a diet of bread and water, housed them in tents and made them wear pink underwear.
In July, Arpaio was convicted of contempt by a district judge after he didn't follow an order to end traffic patrols. A federal court said those stops in search of undocumented immigrants amounted to racial profiling.
He had not been sentenced but in August, White House said in a release that Arpaio's more than 50 years of "admirable service" made him a "worthy candidate for a presidential pardon."
Arpaio, who said he he has not discussed his Senate bid with Trump, said he's ready for a tough campaign.
"I am outspoken. I'm looking forward to it. Let them come. They'll have their political firing squads and bring tons of money here, because they don't want to lose," he said. "I just want to do everything I can to support our president."
In the Republican primary, Dr. Kelli Ward, a conservative activist who attempted to defeat Sen. John McCain in a 2016 primary, is running and Rep. Martha McSally, R-Ariz., is expected to run for the seat.
"Being a U.S. senator is a little different than being the sheriff, because you can do a lot of things in the U.S. Senate, and I have many plans, believe me. It's tough. It's a tough decision. But, if you're going to come across that border, you should be arrested and get the consequences of it," Arpaio said in the interview.
Trump defeated Hillary Clinton by four percentage points in the state in 2016.