The Pontypridd MP, who resigned from the shadow cabinet last month, told the BBC he was "not part of any plot or coup against Jeremy Corbyn" but the leader had rejected compromises he had suggested.
"I think that leaves people like me who love this party and want to see a Labour government to put our hat in the ring and say, 'I can heal this party, I can be a credible Labour leader and the next prime minister'."
Although the former shadow Work and Pensions Secretary said in January: "Jeremy is going to be taking us into the election in 2020. End of", he said MPs had since lost confidence in Jeremy Corbyn's leadership.
Mr Smith will be battling Angela Eagle for the anti-Corbyn vote. She voted for the Iraq invasion. Mr Smith said he was against the war: "I wasn't in parliament at the time. I would have voted against."
At the time, he was working as a special adviser to Paul Murphy, who was secretary of state for Wales and Northern Ireland.
Three years later,  fighting the Blaenau Gwent by-election, Mr Smith told Martin Shipton of the Western Mail : "We are making significant inroads in improving what is happening in Iraq.
"I thought at the time the tradition of the Labour Party and the tradition of left-wing engagement to remove dictators was a noble, valuable tradition, and one that in South Wales, from the Spanish Civil War onwards, we have recognised and played a part in."
Although the Western Mail said at the time that Mr Smith didn't know whether he would have voted against the war, he later made clear that he would have joined the rebellion against Tony Blair's government.
He said on Wednesday he would not vote to hold Tony Blair in contempt of parliament although it was clearly the wrong decision to go to war.
His entry into the contest was welcomed by shadow Chancellor and Corbyn ally John McDonnell, although some Corbyn opponents fear that having two "unity" candidates will allow the current leader to survive.
Some MPs have suggested either Ms Eagle or Mr Smith should withdraw to maximise the chances of defeating Mr Corbyn although neither shows any sign of being prepared to give way to the other.

Carnival had said in March that the sinking of its Costa Concordia cruises ship in January could wipe out profits this year as people shunned cruises.
However, on Tuesday the firm reported that profits were $1.33bn (Â£819m) in the third quarter, compared with $1.34bn in the same period last year.
Shares in the firm in New York rose more than 3%.
Thirty-two people died in the shipwreck in January, which an official report blamed the captain of the Costa Concordia for causing, as well as assigning some responsibility to Costa, which is owned by Carnival.
The Costa Concordia still lies next to the rocky outcrops off Giglio Island in Italy's Tuscan coast.
Carnival said it had managed to generate more money from its cruise passengers.
"The significant efforts of our brand management teams were successful in partially mitigating the decline in cruise ticket prices," said chairman and chief executive Micky Arison.
The company also plans to focus on emerging markets.
"For 2013, the company will capitalise on the increasing popularity of cruising in Asia with the deployment of a second Costa ship in China and the launch of a new Princess Cruises program for the Japanese market," it said.
Costa Cruises is a subsidiary of Carnival and runs some of the company's total fleet of 100 ships. Other brands include Carnival, P&O, Cunard, Holland America, Princess and Seabourn.
Owen Smith has been explaining why he hopes to stand for the Labour leadership.
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Cruise ship operator Carnival has reported profits that beat analysts' expectations, sending shares higher.