Kevin Kearney, 46, had been missing since Tuesday and his body was pulled from the water at about 3.30pm on Wednesday.
Police say the father-of-four took his 17-year-old daughter to school on Tuesday morning and then went to the park to walk the dogs, with the shooting thought to have taken place at about 9.15am.
"The dogs returned to the Dunmore area without Mr Kearney. A relative contacted police at 8pm on Tuesday night to say he was missing," the officer leading the murder investigation said.
Detective Chief Inspector Justyn Galloway added: "Local police began to make inquiries and conducted a number of searches in the area, which resulted in the discovery of Mr Kearney's body.
"He had been shot."
Police are looking to speak to anyone who saw Kevin Kearney in the park on Tuesday, or anyone who saw a silver Peugeot 406 car in the Alexandra Park area that morning.
"Its registration number is GNZ 8168. This car was found burnt out at Donore Court in the New Lodge area around 9.30am on Tuesday," DCI Galloway said.
Police believe Mr Kearney was targeted for the "callous and cold-blooded" murder.
A dissident republican group is suspected to have been involved.
Those responsible claim to be dissident republicans. They are not republicans of any shade. They are entirely motivated by criminal intent.
Deputy First Minister Martin McGuinness
Secretary of State for Northern Ireland Theresa Villiers branded the shooting - and that of another man in Londonderry on Thursday morning, also suspected to have involved paramilitaries - "abhorrent and brutal".
She added: "This type of cowardly vigilante justice is never a substitute for policing and the force of law.
"I send my sincere sympathies to the families of both victims. I strongly encourage anyone who has information about these despicable crimes - and similar ones like the horrific shooting attack in East Belfast last week - to come forward and speak to the PSNI.
"And I am sure the police will leave no stone unturned in bringing to justice the people responsible for these disgraceful attacks."
The Irish News reports that it received a claim of responsibility for the killing, in a statement from a group calling itself 'the IRA'.
The newspaper quotes the paramilitaries as saying they "carried out an investigation" before shooting the man "in response to complaints within our community".
Police say there can be no justification for the murder, regardless of the victim's lifestyle.
Deputy First Minister Martin McGuinness has condemned both the killings in Belfast and Derry.
"I condemn these murders without equivocation," the Sinn Féin politician said.
"Many of these gangs are involved in the drug trade themselves. They are routinely extorting money from drug dealers and other criminals. They are heavily involved in all sorts of organised crime.
"Yet they carry out murders like the ones we have witnessed in Belfast and Derry under the bogus notion that they are standing up for the community."
Mr McGuinness added: "The community have already made their stand. They have stood against gangsterism and criminality and stood for peace and building a new future.
"The community now need to work with the PSNI to bring forward information to allow them to tackle criminality and the criminal gangs who seek to profit on the backs of ordinary decent people."
There can be no justification whatsoever for taking a life and no excuse those carrying out this murder can offer will fill the void in his family.
Justice Minister David Ford
News of the north Belfast killing has caused shock in the local area.
DUP MP Nigel Dodds said: "The entire community will share in the sense of shock at this appalling news. Our thoughts are with the family of the deceased. I appeal for anyone who can assist the police investigation to pass on whatever information they have."
SDLP councillor Pat Convery said: "This is a very tragic event. My thoughts and prayers are with the man's family. I would appeal for anyone who has any information that could help further the investigation to notify the police."
Alliance councillor John Blair added: "This is appalling news, which will send shock waves through the entire community. My thoughts are with the victim's family and friends at this extremely sad time."
Detectives from the PSNI's Serious Crime Branch are leading the investigation and have asked anyone who was in Alexandra Park between 8.30am and 9.30am on Tuesday to get in touch.