A photo of the suspect, Imran, that has been circulating on the internet.
"Our collective effort has borne fruit and the murderer has been arrested," a triumphant Sharif announced to loud applause.
The Punjab CM thanked various ministers, officials and civilian and military intelligence agencies for tracking down the rapist after a 14-day effort.
He said DNA samples from 1,150 people were profiled and once the culprit was caught, his DNA matched a "100 per cent" with the samples collected from the crime scene.
Also read: The child rape victims of Quetta
Sharif also said the suspect was given a polygraph test earlier today, which leaves only 5pc doubt as to his culpability. However, he said the suspect had "accepted all of his deeds" during the test which removed any remaining doubt.
The case "is an example for the nation that when we unite, we can achieve anything", Sharif said.
Shahbaz Sharif's complete press conference.
He said while the first phase of the investigation has been completed with the identification of the suspect, the second was to bring this "beast" to justice.
"If it were up to me, as a person who understands some of [Zainab's father's] pain, I would want him hanged on the chowk [square]," the chief minister said, adding that he will request the chief justice of Lahore High Court (LHC) to ensure that the culprit is made an example of.
"If the law allows, he [the rapist] should be hanged at the square."
Sharif said had it not been for the Punjab Forensic Science Agency (PFSA), the suspect would not have been caught. He said a DNA matching conducted for the second time had confirmed that the arrested suspect is the only culprit.
Recalling the processes involved in the investigation of the case, the chief minister said the effort entailed search operations, geo-fencing, forensic analysis of the crime scene, enhancement of videos of the crime scenes, collection of DNA samples, collection of Nadra pictorial data of 300,000 people and gleaning information from labourers and masons. "Scientific and human intelligence" was used during the probe, he added.
Sharif urged other provincial governments and political parties to "not do politics on dead bodies" and instead address the challenges faced by the country collectively.
Asked by a reporter whether Zainab and other children would have been alive today had the serial killer been caught in the first instance, the chief minister said: "I agree with you 100pc, but this is a moment to appreciate. Accountability will take place of the other [seven cases] as well."
The parents of the other seven children will get justice as well, Sharif added.
Arrested suspect is the only culprit: PFSA The director general of PFSA gave a presentation about the scientific analysis of Imran's DNA. He said the suspect's DNA sample had been collected on January 20 and the profiling was completed in two days.
According to the forensics lab official, the random match probability of Imran's DNA profile is one in 178 quadrillion (178,000,000,000,000,000) .
"It means [that] if there are 178 quadrillion male people at one place, [the] chance of having this profile is only 01 which is Imran's DNA profile," he explained.
"World population is 7 billion, [which] means he is the only one on this planet Earth who has this DNA profile."
Speaking at the press conference, Zainab's father, Muhammad Amin, thanked the provincial and federal authorities and said he was satisfied with the result of the investigation.
Residents surround suspect's house
Earlier in the day, Kasur had turned tense as residents surrounded the house of the suspect, Imran, after police said they had arrested him in connection with Zainab's rape and murder.
As a mob began gathering the suspect's house, police also reached the area urging people to remain calm in order to avoid any untoward incident. Television footage showed a contingent of police in riot gear deployed to secure the surrounding area.
Police sources earlier told DawnNews that Imran is a resident of the same area where Zainab's house is located, and lives very close to the victim's aunt's house.
Read more: New CCTV footage shows suspect walking near house of Zainab's maternal aunt
His appearance matched that of an individual seen with Zainab in CCTV footage recovered by police, according to the sources.
He was arrested as part of the investigation much earlier, but was let go, the sources said, following which he fled Kasur. Addressing this point in his presser, Shahbaz Sharif said the suspect had been initially interrogated and during the investigation he made the excuse that he has suffered a heart attack. But he was later caught after the DNA profiling was completed, he said.
Malik Ahmed Khan, a spokesperson for the Punjab government, told DawnNews that the suspect had now been arrested from Pakpattan.
Khan, citing police, said that the suspect used to frequently disguise his appearance. "Sometimes he would keep a beard, sometimes he would wear spectacles, and he would change his clothes," Khan said, adding that some of the suspect's accomplices are also in police custody.
He said that all other suspects who had been arrested earlier were released when DNA reports cleared them.
On January 4, Zainab had gone missing after leaving her house on Kasur's Road Kot area for her maternal aunt's house a few minutes away for religious lessons.
A few days later, the victim's body was recovered from a trash heap. An autopsy confirmed that she was strangled to death. It also suggested that she had been raped before being killed.
Police had confirmed on January 13 that the results of DNA tests carried out in the wake of the rape and murder of Zainab in Kasur indicated the involvement of one culprit in at least seven similar cases that occurred in the district over the past year.
Zainab's rape and murder had sparked outrage in Kasur and across the country. The day her body was found, protesters had taken to the streets in Kasur, agitating against perceived police inaction.