Vice President Pence filed paperwork on Monday declaring his campaign for president in 2024, setting up a challenge to his former boss, Donald Trump, just two years after their time in the White House ended with an insurrection at the U.S. Capitol and Mr. Pence fleeing for his life.

Mr. Pence, the nation’s 48th vice president, will formally launch his bid for the Republican nomination with a video and kickoff event at Des Moines, Iowa, on Wednesday, which is his 64th birthday, according to people familiar with his plans. He made his candidacy official Monday with the Federal Election Commission.