Tillman, who served with the Army Rangers, was 27.
Although the military had not officially confirmed his death, the White House put out a statement of sympathy that praised Tillman as "an inspiration both on and off the football field."
Lt. Col. Matt Beevers, a spokesman for the U.S. military in Kabul, confirmed that a U.S. soldier was killed Thursday evening, but would not say whether it was Tillman. A military official at the Pentagon confirmed it was Tillman.
Tillman was part of a coalition combat patrol that was ambushed near the village of Sperah, about 25 miles southwest of Khowst, a military contact in Kabul told CBS News Consultant Jere Van Dyk.
"That's real tough country," said CBS News Military Consultant Perry Smith. "It's very mountainous country, the government of Pakistan has never really been in control, there are a lot of tribal elements there. There are a lot of elements that support radical groups like al Qaeda. That's where there's been the greatest amount of combat activity over the last few months."
Two other U.S. soldiers on the combat patrol were injured, and an Afghan soldier fighting alongside the Americans was killed.
Former Cardinals head coach Dave McGinnis said he felt both overwhelming sorrow and tremendous pride in Tillman, who "represented all that was good in sports."
"Pat knew his purpose in life," McGinnis said. "He proudly walked away from a career in football to a greater calling."
Tillman left quietly for the mountains of Afghanistan to serve with his brother — to make right, he said, what 9/11 had made so wrong, reports CBS News Correspondent Lee Cowan.
"My great grandfather was at Pearl Harbor, and a lot of my family has gone and fought in wars, and I really haven't done a damn thing as far as laying myself on the line like that," Tillman had said before leaving.
"In sports we have a tendency to overuse terms like courage and bravery and heroes," said Cardinals vice president Michael Bidwill, son of the team's owner Bill Bidwill, "and then someone like Pat Tillman comes along and reminds us what those terms really mean."
Tillman is not the first NFL player to be killed in combat. Buffalo offensive lineman Bob Kalsu was killed by mortar fire during the Vietnam War in 1970.
A memorial was set up outside Cardinals' headquarters in Tempe, Ariz., with Tillman's No. 40 uniform in a glass frame alongside two teddy bears and two bouquets. A pen was left for people to write messages to Tillman's family.
Gov. Janet Napolitano ordered flags at Arizona State University, Tillman's alma mater, flown at half-staff.
"Pat Tillman was an outstanding ASU graduate who understood that we are in a global war, and he volunteered to be part of that," said ASU President Michael Crow.
"He fully understood the risks, yet he went to defend his country, and he gave up his life. Pat was an extraordinary young man who brought credit to us all."
In a statement, NFL commissioner Paul Tagliabue said, "Pat Tillman personified all the best values of his country and the NFL. He was an achiever and leader on many levels who always put his team, his community, and his country ahead of his personal interests."
Former teammate Pete Kendall, the Cardinals' starting center, said Tillman's death was a jolt of the reality regarding the nation's fight in the Middle East.
"The loss of Pat brings it home," Kendall said. "Everyday there are countless families having to get the same news."
Kendall remembered going out with Tillman and his future wife, Marie.
"We had a meal and a couple of beers," Kendall said. "It was a nice night. I really looked forward to buying him another beer sometime down the road."
Arizona Sen. John McCain noted that Tillman declined to speak publicly about his decision to put his NFL career on hold.
"He viewed his decision as no more patriotic than that of his less fortunate, less renowned countrymen who loved our country enough to volunteer to defend her in a time of peril," McCain, a Republican, said in a statement.
"I think he'll be remembered for a long time for what he's done," Robert Gallery, who is expected to be withint the top five NFL draft picks on Saturday, told CBS News Correspondent Cami McCormick.
"A man who gives up a sort he loves to go serve our country is a man with a lot of courage," he said.
U.S. officials, who spoke on the condition of anonymity, said a formal announcement was expected later in the day.
Tillman played four seasons with the Cardinals before enlisting in the Army in May 2002. The safety turned down a three-year, $3.6 million deal from Arizona.
He made the decision after returning from his honeymoon with his wife.
"He knew what was important to him, and he made his decision and stood by it," said quarterback Eli Manning, expected to be a top pick in Saturday's NFL draft.
Tillman's brother, Kevin, a former minor league baseball prospect in the Cleveland Indians' organization, also joined the Rangers and served in the Middle East. They committed to three-year stints in the Army.
Some 110 U.S. soldiers have died — 39 of them in combat — during Operation Enduring Freedom, which began in Afghanistan in late 2001.
Tillman's agent, Frank Bauer, has called him a deep and clear thinker who has never valued material things.
In 2001, Tillman turned down a $9 million, five-year offer sheet from the Super Bowl champion St. Louis Rams out of loyalty to the Cardinals, and by joining the Army, he passed on millions more from the team.
Tillman turned aside interview requests after joining the Army. In December, during a trip home, he made a surprise visit to his Cardinal teammates.
"For all the respect and love that all of us have for Pat Tillman and his brother and Marie, for what they did and the sacrifices they made ... believe me, if you have a chance to sit down and talk with them, that respect and that love and admiration increase tenfold," McGinnis said at the time.
It was not immediately clear when he went to Afghanistan.
The 5-foot-11, 200-pound Tillman was distinguished by his intelligence and appetite for rugged play. As an undersized linebacker at Arizona State, he was the Pac-10's defensive player of the year in 1997.
He set a franchise record with 224 tackles in 2000 and warmed up for 2001's training camp by competing in a 70.2-mile triathlon in June.
Tillman carried a 3.84 grade point average through college and graduated with high honors in 3½ academic years with a degree in marketing.
"You don't find guys that have that combination of being as bright and as tough as him," Phil Snow, who coached Tillman as Arizona State's defensive coordinator, said in 2002. "This guy could go live in a foxhole for a year by himself with no food."
Tillman and his brother Kevin last year won the Arthur Ashe Courage award at the 11th annual ESPY Awards.