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Mr Pence, 63, is set to formally launch his campaign with a video, speech and townhall event in the early voting state of Iowa on Wednesday.
The move pits him against Donald Trump, the man he served in the White House for four years from 2017-21.
The former president is currently polling well ahead in the race.
Most opinion polls show Mr Pence in a distant third place, with support in the low single digits.
The former Indiana governor and congressman is expected to position himself as a continuation of the Trump administration’s conservative agenda, without the baggage.
Mr Pence, who describes himself as “a Christian, a conservative and a Republican, in that order”, was an unswervingly loyal deputy to Mr Trump through much of their four years in office.
But he has distanced himself from his old boss since the riot by Trump supporters at the US Capitol in January 2021.
Mr Trump pressured Mr Pence to overturn Joe Biden’s election victory when he presided over the certification of results in Congress and admonished him for lacking “courage” when he refused.
Some rioters were heard chanting “hang Mike Pence” as they stormed the halls of Congress, and many Trump loyalists view him as a traitor.
The former vice-president said in March that Mr Trump’s encouragement of the rioters had “endangered my family and everyone at the Capitol that day”.
What happens next?
- Candidates for the Republican nomination will hit the campaign trail and begin a series of TV debates in the coming months
- Elections in each state – called primary elections – begin next February
- The person with the most support will be crowned at the Republican Convention in summer 2024
- The winner of the nomination looks likely to face Democrat Joe Biden in the general election in November 2024
Mr Pence has spent months laying the groundwork for his run and is banking on a strong performance in Iowa.
Religious conservatives are an influential voting bloc in the state and, in 2016, helped Texas Senator Ted Cruz narrowly defeat Mr Trump.
Mr Pence’s popularity with evangelical voters was seen as helping to boost his running mate to the White House.
But he will find himself competing for evangelical voters with other candidates in the race, including South Carolina Senator Tim Scott and former US ambassador to the United Nations Nikki Haley.
The Democratic National Committee said Mr Pence’s entry would drag the Republican field “even further to the extremes”, dismissing him as Mr Trump’s “Maga wingman”. Maga stands for Make America Great Again, the Trump campaign slogan.
Florida Governor Ron DeSantis, who is widely viewed as Mr Trump’s chief rival, is currently polling a distant second in the race. Former New Jersey Governor Chris Christie and incumbent North Dakota Governor Doug Burgum are also planning to enter the race this week.
There is growing concern that a crowded field will split the anti-Trump vote and hand the party’s nomination to Mr Trump again.