Merkel had made no secret that she was keen to end her awkward " grand coalition" with the SPD in favour of the Free Democrats.
Ronald Pofalla, general secretary of the CDU, said: "Coalition talks should start as soon as possible ... and it is our goal to have a coalition deal in a month at the latest."
The CDU and its Bavaria-only sister, the Christian Social Union, won 33.8 per cent of the vote, while the Social Democrats took 23 per cent.
It was the SPD's worst parliamentary election result since the second world war.
The Free Democrats captured 14.6 per cent, with the Left Party taking 11.9 per cent and the Greens 10.7 per cent.
That gave the conservatives 239 seats and the Free Democrats 93 in the lower house, for a comfortable centre-right majority of 332 seats to 290.
The Social Democrats won 146, the Left Party 76 and the Greens 68.
It was a significant shift from the 2005 election, in which Merkel's conservatives just edged past the SPD.
A subdued Steinmeier said the result was "a bitter defeat" but vowed to lead a strong opposition.
Thomas Kielinger, a correspondent for the German daily newspaper Die Welt, said that the end of the "grand coalition" would be a good thing for German democracy.
"Political life will now become far more interesting in the next four years than it has been in the last four," he told Al Jazeera.
"We'll have a proper opposition now ... and we'll have a bit of a tug-of-war inside the coalition where the Free Democrats - more pro-market than Mrs Merkel's party - will want to pull her more into capitalist, pro-business stance which will give her pause and might make her unpopular with large sections of German society."
Voter turnout on Sunday was a post-war low of 70.8 per cent, down from 77.7 per cent four years ago.
Al Jazeera's Barnaby Phillips, reporting from Germany, said the low turnout partly reflected the fact that it was not the most passionate of campaigns, that enough Germans felt relatively pleased with the direction their country was going in and that it was hard to discern dramatic policy differences between the parties during the campaign.
The vote took place against a backdrop of heightened security after al-Qaeda issued several videos last week threatening to punish Germany if voters backed a government that kept German troops in Afghanistan.
In foreign policy, a centre-right coalition could be more vocal in trying to block Turkey's bid to join the European Union.
Merkel favours a "privileged partnership" for Ankara that stops short of full membership.
But foreign policy issues were not top of voters' lists going into the election, with the vote coming at a crucial time domestically for Europe's largest economy, just now emerging from its deepest recession of the post-war era.
The next government will have to get a surging budget deficit under control and cope with rising unemployment and the threat of a credit crunch as Germany's fragile banks pull back their lending.