The married father of two was shot when he was ambushed while driving on the M1 motorway on Thursday. Mr Black worked at Maghaberry prison, where republican inmates have been holding protests. He is the first NI prison officer to be murdered by paramilitaries in almost 20 years.
Shops closed and hundreds of people lined the streets as Cookstown came to a standstill on Tuesday, with former colleagues from the prison service and friends from the Orange Order among those who gathered to pay their respects at Mr Black's funeral.
Reverend Tom Greer of Molesworth Presbyterian Church, where Mr Black attended regularly, said he was horrified at the brutality of his murder.
"It is so terrible that evil men with such hatred in their hearts should rob us of a great man like David with love and kindness in his heart," he said.
David Black was a man of honour and principle, a man of kindness and generosity, a man committed to peace and prosperity in Northern Ireland - all those things completely the opposite of the murderous thugs and bloodthirsty criminals who took David’s life.
Rev Greer said former prisoners had spoken of the impact that Mr Black had on their life.
"David viewed his work as something that was meant to improve society. He wanted those who came into prison to leave as changed men."
A private service was held at Mr Black's home, before the family made their way to the church, where his children Kyle and Kyra paid personal tribute to their 52-year-old father.
His teenage daughter read out a poem about her father describing his "big smile and chuckle" which brightened up her day.
The emotional tribute continued: "Our love will be everlasting, that will never ever change.
"But the one thing I want you to know is that I'm so proud of you. You're not just my daddy, but forever my special hero."
Kyle said: "They can take daddy from us. They can deprive Kyra and me of a devoted father and mummy of a loving husband, but they can never take away the love that we have in our hearts and the memories that we will all cherish for the rest of our lives.
"Daddy may not be here in person but he will be here with us all in spirit."
He continued: "Although daddy was small in stature he had had a large impact on the lives of everybody that knew him and he's left a huge legacy - one that my mummy, Kyra and myself will be so, so proud to carry on."
The family were joined at the church by politicians including First Minister Peter Robinson, Ulster Unionist leader Mike Nesbitt and SDLP leader Alasdair McDonnell.
Deputy First Minister Martin McGuinness offered to go to the funeral, but it is believed the Black family asked him not to attend.
A number of other politicians were also at the funeral, as well as the PSNI Chief Constable and the Director General of the Northern Ireland Prison Service and his southern counterpart.
Rev Greer also spoke of the "great dignity" shown by Mr Black's family in the wake of his murder.
"They have determined not to seek revenge or to encourage it in anyone else. They long to see justice done but will not meet other people's bitterness and hatred with any of their own. They set an example to us all," he said.
Presbyterian moderator Dr Roy Patton joined in the condemnation of those who carried out the murder.
"We are together in this, totally united as churches, politicians, civic society, ordinary men and women who feel for you today in your unspeakable loss, and who in the strongest possible terms are outraged by such an evil deed.
"This attack on a prison officer was an attack on this whole community," he added.
Two men questioned by the PSNI about the murder have both been released unconditionally, while a 29-year-old man detained in Co Leitrim was released by Gardaí on Tuesday.