McLennan County Sheriff Larry Lynch provided no other details on the condition of the body or the possible cause of death, but said Dennehy's family had been notified.
The site where the body was found is north of gravel pits where authorities searched after Carlton Dotson, who played basketball at Baylor last season and had been living with Dennehy since spring, was arrested last week and charged with his murder.
CBS News Correspondent Elizabeth Sanchez reports the place where the body was found, near a dirt road, is close to the gravel pits where witnesses last month said they heard gunshots.
Investigators had continued to comb through the high weeds Sunday, collecting evidence in a field where they found Dennehy's decomposed body Friday night.
"With that evidence collected today, they were able to make a positive identification," Lynch said, refusing to specify what evidence was found.
McLennan County Justice of the Peace Belinda Summers told The Associated Press that searchers found a head Sunday morning in the same field where the body was discovered.
On Sunday, authorities used farm equipment to cut down tall weeds and grass, some as high as 7 feet tall, in a rural area about five miles south of Waco.
The body found Friday was taken to the Dallas County Medical Examiner's Office for autopsy.
Dotson, 21, was arrested last week in his home state of Maryland on a murder charge from Texas. He is being held without bail, awaiting a hearing on extradition to Texas.
Even if he fights extradition from Maryland to Texas, says CBSNews.com Legal Analyst Andrew Cohen, it won't hold up the proceedings for very long. In the end he'll almost certainly lose that battle and be brought back to face the murder charge.
"I suspect his attorneys know that as well and are going to want to focus upon more substantive issues as they try to defend him," Cohen said.
The defense will have some facts and issues to work with, including the issue of whether Dotson is competent to stand trial or whether he was legally insane at the time of the alleged shooting. Also, it's not inconceivable that a jury might believe that the shooting, if Dotson did it, was an accident or self-defense given the circumstances.
Dotson was arrested July 21 after calling 911, saying he needed help because he was hearing voices, authorities said. Waco police said Dotson told FBI agents in Maryland that he shot Dennehy after the player tried to shoot him. But after his arrest, Dotson told a reporter that "he didn't confess to anything."
Dotson's personality suddenly changed in November, and at times he described himself as a prophet and said he saw visions, his estranged wife told the Star-Telegram. Melissa Kethley said her mother was so concerned about Dotson's mental state that she wrote a letter to a Baylor coach in early June.
Baylor coaches knew about Dotson's increasing mental troubles because they arranged for him to see a therapist this spring, Kethley told The Dallas Morning News for a story in its Saturday editions.
Between January and March, Dotson went three or four times, Kethley said. She said Dotson liked his therapist but never told him about the voices that he heard, his visions or fears that his wife was unfaithful.
"I used to say, 'You just need some kind of help,' because he could go from nice to outrageously mad in a matter of seconds for no reason at all," said Kethley, who separated from Dotson in April.
Dennehy, 21, had not been seen since mid-June.
Dotson and Dennehy arrived last summer in Waco, about 100 miles south of Fort Worth, on basketball scholarships. Baylor is the world's largest Baptist university with 14,000 students.
Dotson was a transfer from Paris Junior College in East Texas and eligible to play. Dennehy, because of NCAA eligibility rules, had to sit out a year after transferring from New Mexico, where he was kicked off the team for losing his temper.
Dennehy's family reported him missing June 19, about seven days after he was last seen on campus. Dennehy's vehicle was found abandoned in a Virginia Beach, Va., parking lot June 25.
An unnamed informant told Delaware police that Dotson told someone that he shot Dennehy in the head as the two argued while shooting guns in the Waco area, according to court documents filed in the case June 23.
Baylor President Robert Sloan notified faculty, staff, students and alumni about the identification Sunday night, saying in an e-mail that "today our worst fears were realized." He asked Baylor employees to pray for Dennehy's family and for Dotson.
"Baylor has endured the heart-wrenching loss of students before, but never in such a startling and perplexing manner," Sloan wrote. "We grieve the loss of Patrick and the impact of that loss on the Baylor community."
Dennehy's stepfather, Brian Brabazon, says the family is praying for his accused killer.
"He's suffering, too," said Brabazon.