He wrote in a letter to Republican colleagues that they "have an opportunity to turn the page".
Mr Ryan, who is widely expected to win the race to succeed John Boehner, will face elections next week.
If victorious, he will have a key role in US politics, second in line to the presidency and tasked with avoiding a looming government shutdown.
The House of Representatives, the lower chamber in the US Congress, has major budgetary and spending deadlines on the horizon.
If Congress fails to pass a budget by early December, the government could shut down again, as it did in 2013.
"I know you're willing to work hard and get it done, and I think this moment is ripe for real reform," said Mr Ryan in the letter.
"I believe we are ready to move forward as a one, united team. And I am ready and eager to be our speaker."
Earlier this week, Mr Ryan had said he wanted endorsements from all key elements within the Republican party to guarantee he could try to unify the party in the House after deep divisions emerged.
The 45-year-old from Wisconsin was the Republican vice-presidential nominee in 2012.
Congressman Paul Ryan will run for speaker of the US House of Representatives, he has announced.