PC Gavin Smith, who appeared on Channel 5's Police Interceptors, died from cancer aged 34 on 15 February.
Mr Smith, who lived in Bishop Auckland with his wife Kezi and daughter Tilly, four, joined Durham Police in 2004.
Officers formed a guard of honour to accompany his cortege from Durham Market Square to the cathedral.
Insp Ed Turner of the roads policing unit said: "Gav was one of those characters who just put everybody at ease, no matter who was in his company.
"The station was always a more lively place when he was there. He had one of those infectious personalities.
"He would always put others before himself and right to the end he was focused on ensuring that Kezi and Tilly were OK and they would be provided for.
"In Gav we have not only lost a dedicated police officer, but a true friend."
He died at home surrounded by his family.
At the time, his widow Kezi said: "It has been a real comfort to both me and Tilly that he was so well regarded by so many.
"We will both miss him so very much."

Gammon joints, 700 pigs in blankets, cash and four charity boxes were also taken from MD Griffiths in Dinas Powys.
Butcher Mark Griffiths, 62, said: "For some families their whole Christmas spread has been taken."
He said he was in talks with wholesalers to try to replace what was stolen.
Father-of-five Mr Griffiths, who has run the butcher's shop for 18 years, said: "There's never a good time for this to happen but during our Christmas rush it's particularly bad.
"We lost turkeys, ducks, chickens, pigs in blankets - all the trimmings that make this time of year so special."
"It's affected 25 orders but I'm determined not to let our customers down."
Mr Griffiths discovered the break-in at 05:00 GMT on Friday when he noticed the panel on the door had been forced open.
He said: "This is a family business and we are gutted to have been targeted in this way.
"Customers have been back and forth to the shop to ask about their orders and we are doing what we can to recoup our loses."
Customer Rowan Young, 50, described the thefts as "sickening", adding: "If we are the unlucky ones whose meat has gone then we fully understand."
The funeral of a police officer who appeared in a TV documentary series has been held at Durham Cathedral.
[NEXT_CONCEPT]
Dozens of families could be without their Christmas dinner after thieves stole turkeys from a butcher's shop in Vale of Glamorgan.