"Honestly I can never remember a point in my life where I felt more relieved," said Tampa Police Chief Jane Castor.
Police said Morris also was suspected in two other slayings, and by early Saturday he faced a third murder charge in the May 18 shooting death of a man killed outside his family's Tampa apartment. A statement from Tampa police Public Information Officer Laura McElroy said ballistic tests indicate the same gun was used in the officers' killings this week.
Morris was scheduled to make his first court appearance Saturday. Officials did not know whether he had an attorney.
Hundreds of officers in tactical gear had combed apartment buildings, vacant homes and even waterways during an intense manhunt for Morris following the officers' deaths. Detectives fielded more than 400 tips.
McElroy's statement said the surrender came nearly 30 hours after detectives began negotiations with an associate of Morris.
"Detectives continued a dialogue with the associate that eventually led to Dontae Morris turning himself in," the statement said. The associate will be entitled to a $100,000 reward that had been offered for information leading to his arrest, it said.
A short time later, police also announced that Morris' 21-year-old brother was arrested early Saturday morning at a Tampa motel on charges of domestic violence and cocaine and marijuana possession.
News of the surrender and charges came just hours after a wake for officers Curtis and Kocab drew hundreds of mourners to a crowded church. Photographs of Curtis with his wife and four sons were shown on large screens. Kocab was pictured with his wife, who is nine months pregnant.
Funerals for the two men, who were both 31, were scheduled for Saturday.
It was about 2:15 a.m. Tuesday when Curtis pulled over a man and woman in a red Toyota Camry. He called for backup after seeing the man was wanted in Jacksonville for writing a bad check. Six minutes after Curtis and Kocab approached the car's passenger side, a witness called 911 to report they were shot. The officers were pronounced dead at a hospital.
The car's driver, Cortnee Brantley, was charged Friday with a federal count of witnessing a felony and not reporting it. Officials also did not know whether she had retained an attorney.
In the May 18 shooting in which Morris is charged, 21-year-old Derek Anderson was killed outside his family's apartment after detectives believe the shooter tried to take Anderson's backpack.
Hillsborough County Sheriff David Gee said Friday night that Morris also is considered a suspect in the June 8 death of father of four who was found severely injured on the side of a road and died en route to a hospital.
Authorities are looking into why Morris was released from prison in April and not transferred to Jacksonville, where warrants had been issued in the bad check case. Corrections officers informed Jacksonville authorities of Morris' impending release last October, prison records showed. Jacksonville Sheriff John Rutherford has said his office is looking into the matter.