President Bush gave Martinez his blessing at a meeting in the Oval Office, calling the Cuban-born senator an American success story.
"He's going to be an excellent spokesman for the Republican Party," Bush said. "He'll be a person who'll be able to carry our message as we go into an important year in 2008."
Martinez will keep his U.S. Senate seat representing Florida and be the voice of the Republican Party going into the presidential election campaign season.
The day-to-day operations will be run by Mike Duncan, who will be chairman. Both have to be formally elected by the Republican National Committee in January.
Martinez said the contest should be about "a battle of ideas" and not partisanship. He said there was an agreement not to show preferences for any candidate in the 2008 presidential campaign before the party's nominee was chosen, allowing the field to sort itself out.
"One of the things that I made clear as I discussed this job role with the president is I was not going to be an attack dog, and I don't intend to, and I wasn't asked to be one," he told reporters at the White House.
"It's not an easy time for our party. It's time for us to come together and pick ourselves up and look to the future and be the party of hope and opportunity that we've been in the past," he said.
Martinez would not comment on where Republicans went wrong in the Nov. 7 congressional elections, in which they lost power in both the Senate and House to Democrats.
"I am not going to do a post-mortem," he said. "As I said, I'm going to be looking to the future."
But Martinez, who came to the United States from Fidel Castro's Cuba in 1962 at age 15, said his party had made mistakes on the immigration issue.
He helped forge a compromise in the Senate this year to revamp immigration laws, only to see it stall in the House.
"I think we didn't always strike the right tone on that and I think that was a mistake," Martinez said.