Mr Abbott told a jubilant crowd at the Four Seasons ballroom in Sydney it was time for "measured reflection on the magnitude of the task ahead".
"There should be no premature triumphalism," he said.
Prime Minister Julia Gillard earlier declared the election "too close to call" and congratulated independent MPs who could be vital in the likely case of a hung parliament.
Mr Abbott, whose speech was punctuated by repeated chanting of "Tony, Tony, Tony", thanked the Australian people for their commitment to democracy, no matter who they voted for.
Mr Abbott said he was proud of every coalition supporter around the country.
"I have to say to you that I feel humbled as I think of the responsibilities that could lie ahead."
The opposition leader singled out Nationals leader Warren Truss, deputy Liberal leader Julie Bishop, the Liberal party president Alan Stockdal, campaign director Brian Loughnane and opposition treasury spokesman Joe Hockey in his round of thank yous.
Mr Abbott thanked party members and supporters, and recognised Ms Gillard, saying it had not been an easy eight weeks for her as prime minister.
"She has certainly worked extremely hard for her cause under difficult circumstances," he said.
Mr Abbott said Labor had definitely lost its majority.
The declaration was greeted by more cheers of "Tony, Tony, Tony."
"And what that means is that the government has lost its legitimacy," he said.
A government which found it hard to govern effectively with a 17 seat majority would never be able to govern effectively in a minority government, Mr Abbott said.
The number of votes Labor had picked up at this election was "a great fact," Mr Abbott said.
"We do not have a clear result from tonight, and I want to say that until a clear result has emerged from this election, that the caretaker conventions under which the government has been operating for the last five weeks must continue," he said.
Mr Abbott said the election had been a win for the public, whose judgment must always be respected.
Mr Abbott said the Labor Party had achieved the lowest primary vote of any governing party since World War II.
Australians had also responded to coalition policies, he said.
Mr Abbott called the election a "referendum on the political execution of a prime minister", referring to Kevin Rudd.
"The Australian people have said that whatever else might characterise our political culture, it should never be characterised by the knock on the door at midnight from the faceless men of the Labor factions," he said.
Mr Abbott declared the coalition back in business, to wild cheering.
"The Liberal and National parties are back in business, we stand ready to govern, and we stand ready to offer the Australian people stable, predictable and competent government," he said.
Mr Abbott said he would talk to independent lower house members in the coming days, to ensure that a federal government could be formed in the event of a hung parliament.
Mr Abbott thanked his own staff for working "so incredibly hard" over the past nine months "and on whose hard work tonight's result rests".
"But it has been a team effort," he said.
"I am the leader of the team but it has been a team effort and this is a very strong team."
The Liberal leader thanked all candidates who'd been elected.
Then singled out the Liberal candidate for Hasluck in Perth - indigenous health and education adviser Ken Wyatt.
"It looks likely that the first ever indigenous member of our House of Representatives will be a Liberal member."
