Rossi, 44, had been deliberating on whether to run for months. He emerged as the GOP's top choice after several other high-profile prospects bowed out.
"I intend to run," he said in an interview. "My analysis is that, yes, I can win it. I wouldn't be moving down this path if I didn't think I could win."
He said Democrats have held the governor's mansion for 20 years and it's time for a change.
Rossi, a real estate investment broker, sprang to prominence this year after Republicans took control of the state Senate. As chairman of the powerful Ways and Means Committee, he was a chief architect of the no-new-taxes budget adopted by the Legislature.
The only other candidate in the Republican primary is Dr. Federico Cruz, director of the Tacoma Pierce County Health Department. Three Democrats are running to succeed Gov. Gary Locke: former Supreme Court Justice Phil Talmadge, King County Executive Ron Sims, and Attorney General Christine Gregoire, who is widely considered the favorite.
Rossi said he will make his formal announcement later this month, but was filing papers with the Public Disclosure Commission on Monday.
"This is my first step toward running for governor," he said.
Rossi had been weighing three factors before jumping in: Whether it would work for his family, whether he could raise $4 million or more to run the campaign, and lastly, whether he could win. All ended up being positive answers, he said.
"Actually, in the end, my wife, Terry, as usual, said something that jelled the decision. She asked, `What kind of state do we want our kids to take?' Our kids are 13, 9, 7 and 3, and we know that our state is going in the wrong direction and that I'm in a position to actually do something about it.
"My grandfather was a coal miner in Black Diamond, my father was a Seattle public school teacher and I'm born and raised here, and the thought of my children having to leave because they can't find employment is unacceptable."
Rossi said he's been all across the state testing the waters for his campaign - and found strong encouragement from people who want a change. The last Republican to win the top office was John Spellman in 1980.
An internal poll showed that 66 percent of the voters think the state is on the wrong track.
"Democrats have had 20 years and we're broke and out of work. It's time to turn the economy around and put people back to work."
He said he can boost the economy by making Washington a more competitive state for business and to attract investment from out-of-state.
Rossi said he's a "fiscal conservative with a social conscience," and that the budget he produced earlier this year showed his stripes.
"The goal this last year was to not raise taxes and still to protect the poor and the vulnerable. We met that goal."
Rossi, whose mother raised her five older children in Seattle public housing, received a business degree from Seattle University in 1982. He was first elected to the state Senate in 1996 and re-elected in 2000.
He quickly rose through the ranks of the Senate, becoming budget chairman this year. He has been mentioned for majority leader if Jim West wins Spokane's mayoral race on Tuesday.
"I'm very excited about this," Rossi said. "It will be a whole new adventure. I'm looking forward to the challenge."