Martinez, a first-term senator, will be the face of the party, focusing on fundraising, outreach and travel to promote the GOP agenda.
The current party chairman, Ken Mehlman, is leaving his post in January at the end of his two-year term.
As a team, Martinez and Duncan will be responsible for leading the RNC during Bush's final two years in office and throughout the 2008 presidential election cycle.
Splitting the chairmanship in two is not new.
President Reagan once chose Sen. Paul Laxalt of Nevada to be general chairman while Frank Fahrenkopf was chairman, and President Clinton initially had Sen. Christopher Dodd of Connecticut and Don Fowler share the Democratic Party role in the same fashion.
Kerry Feehery, a Martinez spokeswoman, and her counterparts at the RNC declined to comment.
By tapping Martinez to be the party's public persona, the White House turned to a lawmaker who has been a staunch supporter of the president — including on the issue of comprehensive immigration reform that includes a guest-worker program — and one of the more politically savvy Republican senators.
Martinez, of Cuban descent, will fill the post as the GOP is seeking to make inroads with Hispanics, considered a swing voting group. He is one of three Hispanics in the Senate along with Democratic Sens. Ken Salazar of Colorado and Bob Menendez of New Jersey.
In last week's elections, exit polls conducted for The Associated Press and the networks showed 69 percent of Hispanics voted for Democrats compared with 30 percent for Republicans, a decline for the GOP compared with 2004 when Bush got about 40 percent of the Hispanic vote.
Martinez served as Bush's secretary of Housing and Urban Development from 2001 until 2003, when he resigned to run for the Senate seat left open by Democratic Sen. Bob Graham's retirement.
In a race marked by hard-hitting television ads and squabbling over Iraq, Martinez was elected with 49 percent of the vote — a slim margin that was credited to Bush's win in that state.
Early in his Senate tenure, Martinez faced a politically unflattering situation.
A Martinez aide wrote a one-page unsigned memo that laid out the political benefits of getting involved in the fate of Terri Schiavo, a Florida woman whose end-of-life battle became a rallying cry for conservatives. Senate Republicans disavowed the memo. Its author resigned.
Before serving in the Cabinet, Martinez's national profile was raised as the drama surrounding a Cuban boy named Elian Gonzalez unfolded in 2000.
The top county official in Orange County, Fla., at the time, Martinez argued on national television talk shows and before a U.S. Senate committee that the boy should stay in the United States. He also invited Gonzalez to Walt Disney World before the boy was returned to Cuba.
For his part, Martinez fled Cuba in 1962 as a 15-year-old. His parents remained on the communist island, hoping one day to join him. He eventually was placed with a foster family in Orlando, studied English and worked odd jobs that helped him buy his father a used car when his parents arrived in the United States four years later.
Martinez put himself through college, earned a law degree, and eventually made millions as a trial lawyer before entering politics.