Editor's note, 9:57 p.m. EDT: The White House has issued the following response to this story, attributed to White House National Security Advisor James Jones:
"Reports that President Obama has made a decision about Afghanistan are absolutely false. He has not received final options for his consideration, he has not reviewed those options with his national security team, and he has not made any decisions about resources. Any reports to the contrary are completely untrue and come from uninformed sources."
Tonight, after months of conferences with top advisors, President Obama has settled on a new strategy for Afghanistan. CBS News correspondent David Martin reports that the president will send a lot more troops and plans to keep a large force there, long term.
The president still has more meetings scheduled on Afghanistan, but informed sources tell CBS News he intends to give Gen. Stanley McChrystal most, if not all, the additional troops he is asking for.
McChrystal wanted 40,000 and the president has tentatively decided to send four combat brigades plus thousands more support troops. A senior officer says "that's close to what [McChrystal] asked for." All the president's military advisers have recommended sending more troops.
But they also have warned that troops alone will not win the war unless Afghan President Hamid Karzai cleans up his government.
"He's got to take concrete steps to eliminate corruption," Adm. Michael Mullen, chairman of the Joint Chiefs of Staff said last week. "That means you have to rid yourself of those who are corrupt. You have to actually arrest and prosecute them."
The first combat troops would not arrive until early next year and it would be the end of 2010 before they were all there. That makes this Afghanistan surge very different from the Iraq surge, in which 30,000 troops descended on Baghdad and the surrounding area in just five months.
Karzai Vows to Tackle Corruption, Cronyism
Opinion: Afghanistan: Obama's First Domino
U.S. Troops to Afghanistan: A Waiting Game
Obama Eyes Smaller Afghan Troop Option
On Afghanistan, a Decision Comes Slowly
Obama Nears Decision on Afghanistan Troops
Obama: I Won't Rush Afghanistan Decision
Fred Kagan of the American Enterprise Institute says a slow motion surge will produce slow motion results.
"If they're going to be sort of trickled in very slowly over the course of a year than it's unlikely to have a very decisive impact in the course of 2010," he said.
The buildup would be expected to last about four years, until McChrystal completes his plan for doubling the size of the Afghan army and police force.
With 68,000 Americans already there, the Afghan surge would mean there would be 100,000 U.S. troops in Afghanistan by the end of the president's first term.
The president is not expected to announce his decision until after he returns from China the week before Thanksgiving.