Mr. Johnson, who is 66 years old and once pledged to retire after this term, made his announcement in an opinion column published Sunday in The Wall Street Journal.

“I believe America is in peril,” Mr. Johnson wrote. “Much as I’d like to ease into a quiet retirement, I don’t feel I should.”

The former businessman has cast himself as an outsider and has tried to establish himself as a leading voice for fiscal restraint, while also embracing Mr. Trump’s false claims of widespread election fraud in 2020. He has opposed Covid-19 vaccine mandates and questioned the push to vaccinate as many people as possible, citing possible safety concerns.

In announcing his bid, he pointed to the pandemic and what he described as the government’s failed response, criticizing the “tyrannical approach taken by the elites who have created and maintained a state of fear that allows them to exercise control over Americans’ lives.”

Democrats are defending 14 Senate seats this year, compared with 20 for the GOP. The nonpartisan Cook Political Report is forecasting that a half dozen will be highly competitive: Arizona, Georgia, Nevada, North Carolina, Pennsylvania and Wisconsin.

Mr. Johnson’s decision to seek a third term made clear that incumbents would be running in four of those six states. North Carolina and Pennsylvania are the exceptions and feature crowded primaries for both parties.

President Biden’s sagging approval ratings have Democrats worried about keeping control of Congress, as the party that holds the presidency traditionally loses seats in midterm elections. Moreover, voters are feeling squeezed by inflation and worried about uncertainty over the pandemic, even as the job market remains strong.

“Senate Republicans clearly feel bullish on their chances for retaking the majority,” said GOP consultant Alex Conant.

Reflecting the expected intensity of the race in Wisconsin, the Democratic Senatorial Campaign Committee had within hours of Mr. Johnson’s announcement rolled out a digital attack ad it said was part of an initial five-figure campaign.

“In 2022, Wisconsinites will hold Ron Johnson accountable and elect another Democratic senator who will put the interests of our state’s working families first,” said Democratic Party of Wisconsin Chair

Ben Wikler

in a statement.

Mr. Thune, the Senate’s No. 2 Republican, made his announcement Saturday, and is seen as having a clear path to re-election. He has drawn the wrath of Mr. Trump for pushing back on the former president’s false election fraud claims. At the same time, he is popular among Senate Republicans and seen as a leading contender to one day succeed Senate Minority Leader Mitch McConnell (R., Ky.).

In the weeks leading up to Mr. Thune’s decision, his colleagues launched a behind-the-scenes campaign to encourage him to run again, people familiar with the effort said.

The 61-year-old angered Mr. Trump after the 2020 election when he predicted that any attempt to block ratification of Mr. Biden’s win in a joint session of Congress would “go down like a shot dog.”

Mr. Trump responded by calling for a primary challenger for Mr. Thune. He also accused Mr. Thune of being a RINO, or “Republican in name only,” and urged South Dakota Republican

Gov. Kristi Noem

to challenge him, something she declined to do.

Mr. Johnson is facing a trickier road to retaining his seat, with state polling showing him underwater. A Marquette Law School Poll of registered voters in late October showed 38% said they would vote to re-elect Mr. Johnson, while 52% said they would support someone else.

Close to a dozen Democrats are jockeying ahead of an August primary to win the right to challenge Mr. Johnson in the general election. Based on early fundraising figures, the top four Democrats in the race are Lt. Gov. Mandela Barnes and State Treasurer Sarah Godlewski, as well as Alex Lasry, the son of a billionaire hedge-fund manager who is also co-owner of the Milwaukee Bucks basketball team, and Tom Nelson, the top elected official in a county southwest of Green Bay.

With a significant number of swing voters, Wisconsin has elected both progressives and conservatives to statewide office. In 2018, it re-elected Democratic

Sen. Tammy Baldwin,

one of the chamber’s most liberal members, by almost 11 percentage points, while also only barely voting conservative Republican Gov. Scott Walker out of office. Mr. Biden won Wisconsin in 2020 by six-tenths of a percentage point, the third-narrowest outcome nationwide.

Mr. Johnson won his seat in 2010 by defeating former Democratic Senator Russ Feingold, a three-term incumbent. Mr. Johnson won a rematch between the two men six years later, although his 2016 margin was narrower.

The state saw some of the first television advertisements of the 2022 campaign cycle nearly a year ago when the Democratic Party of Wisconsin launched more than $100,000 in spots critical of Mr. Johnson.

—Lindsay Wise contributed to this article.

Write to John McCormick at mccormick.john@wsj.com