"If you think that there's something absolutely critical, try as hard as you can and let the chips fall where they may and that's exactly what I'm doing," Steyer said in a video announcing his run for the White House, the Efe news reported.
The 62-year-old political activist, who made his fortune as a hedge fund manager, made his announcement hours after Rep. Eric Swalwell, another Californian, said he was dropping out of the race to win the Democratic nomination and the right to take on Trump.
Steyer said he was motivated to run because the United States had a "broken political system."
"Almost every single major intractable problem, at the back of it, you see a big money interest for whom stopping progress, stopping justice is deeply important to their bottom line," Steyer said.
Steyer, like Trump in the 2016 elections, said that as an outsider, he could change the political system and could not be bought.
The billionaire activist, who has pledged to give away half of his fortune to charity, has long been a big donor to Democratic candidates and liberal causes.
Steyer and his wife, Kat Taylor, according to the Center for Responsive Politics, have given more than $238 million to political campaigns and groups, putting them in the No. 2 spot on the list of large donors, trailing only casino mogul Sheldon Adelson and his wife.
Steyer said that if elected, he would make addressing climate change a priority of his administration.
In January, Steyer travelled to Iowa, where the Democratic primary season will start in February 2020, leading to speculation that he might join the crowded field of candidates already vying for the nomination.
The California billionaire, however, said at the time that he would not run for the president, opting to instead focus on impeaching Trump and removing him from office.
Swalwell's announcement on Monday in Dublin, a city in the San Francisco Bay area, that he was dropping out of the presidential race left 24 candidates still competing for the nomination, with many of them polling in the low single-digits.
The congressman's presidential campaign lasted exactly three months.
( With inputs from IANS )