The encounter follows Obama's promise, in the aftermath of the bitterly fought Nov. 6 election, to consult the former Republican governor of Massachusetts by the end of the year. It also comes amid Obama's efforts to work out with congressional leaders a way to avoid a looming "fiscal cliff" that could push the U.S. economy back into recession.
"Governor Romney will have a private lunch at the White House with President Obama in the private dining room," the White House said of the meeting, which will be closed to the media. "It will be the first opportunity they have had to visit since the election."
Obama's talks with Romney will be sandwiched between a series of events this week in which he is making his case to Americans to raise taxes on wealthy Americans while extending tax cuts for the middle class - an approach that his former Republican rival strongly opposed during the campaign.
Obama's Democrats and their Republican foes remain deadlocked over dramatic, year-end tax increases and spending cuts known as the fiscal cliff that will kick in unless a deal is struck.
Seeking to make good on his post-election pledge to reach across the political aisle, Obama told a news conference he wanted to "sit down and talk" to Romney to hear his ideas and see whether they could work together.
Obama said he could envision a future role in public service for Romney but had no specific "assignment" for him.
Romney, in a conference call with donors after the election, was widely reported to have said that Obama won by using targeted initiatives to reward specific constituencies, including African-Americans, Latinos and young people.
Obama, who won a decisive victory after a bruising campaign, had sought to depict Romney as out of touch with ordinary Americans and intent on shielding the rich from higher taxes.
Romney had accused Obama of failed economic policies and wasteful spending to promote big government.