Republican officials say the announcement - the latest chapter in a shakeup of President Bush's team - could come as early as Wednesday.
The Washington Post quotes sources familiar with the negotiations as saying that Snow decided to accept the offer after top officials assured him that he would be an active participant in administration policy debates as well as a spokesman.
Snow would be replacing Scott McClellan, who is stepping down in a White House makeover intended to re-energize Bush's presidency, bring in new faces and lift the president's record-low approval ratings. McClellan has served as President Bush's chief spokesman — the most prominent public figure in the White House after Mr. Bush — for nearly three years.
Snow, a Fox News commentator, has written and spoken frequently about the current president — although not always in a complimentary way.
The Center for American Progress, a liberal think tank, circulated unflattering observations by Snow about Bush.
"His (Bush's) wavering conservatism has become an active concern among Republicans, who wish he would stop cowering under the bed and start fighting back against the likes of Harry Reid, Nancy Pelosi and Joe Wilson," Snow wrote last November after Republicans failed to win the governor's race in Virginia. "The newly passive George Bush has become something of an embarrassment."
Last month, Snow wrote that President Bush and the Republican Congress have "lost control of the federal budget and cannot resist the temptation to stop raiding the public fisc. (treasury)"
Snow, in an Associated Press interview on Tuesday, said: "It's public record. I've written some critical stuff. When you're a columnist, you're going to criticize and you're going to praise."
He declined to say whether he had been offered the White House job. Republicans close to the White House said the press secretary's job had been offered to Snow and that he has accepted. They spoke on condition of anonymity.
One factor in the timing of Snow's decision is said to be a battle last year with cancer, involving six months of chemotherapy. He had a CAT scan last week and is said to have delayed a decision on the White House job until he had a chance to consult with his doctors.
Snow is the host of the "Tony Snow Show" on Fox News Radio and "Weekend Live with Tony Snow" on the Fox News Channel. He served in the administration of President George H.W. Bush, as White House speechwriting director, and later on as a deputy assistant to the president for media affairs.
Brit Hume, Fox's Washington managing editor, told the Washington Post that he was "a little surprised" that Snow would forgo a leave a brand new radio show to take on one of Washington's most demanding jobs.
"I think he's excited by the idea of being on the inside," Hume told the Washington Post. "He believes he will be at the table when decisions are made. For someone of his bent, that's too good to pass up."