Dr Kidman, a respected clinical psychologist, died last week in Singapore, aged 75 after collapsing of a suspected heart attack.
Nicole Kidman and Keith Urban sang Amazing Grace at her father's funeral
The actress sang an acoustic version of Amazing Grace with husband Keith Urban, whispering 'thank you' as the last chord was played.
She had earlier told the congregation: "He was the father who was always going to be there".
In her touching tribute the Oscar-winning star remembered his final visit to her three weeks ago in New York, telling a funny story about how he ate all the pizza they had been due to share together and was very apologetic.
"I am so grateful he came to New York. And I'm so glad he ate all that pizza," she said to laughter.
At the service in St Francis Xavier Church on Sydney's North Shore, Nicole was also accompanied by her two daughters with Keith, Sunday Rose, six, and Faith Margaret, three. Her two adopted children from her marriage to Tom Cruise, Isabella and Connor did not attend.
Her sister Antonia arrived with her husband Craig Marran and six children. The ceremony also included the hymn Morning Has Broken and the poem Farewell by Anne Bronte.
Nicole Kidman and Keith Urban were accompanied by their daughters at the final farewell
When the service was over The Carnival Is Over by the Seekers rang out. Keith and Craig led the pallbearers who also included fellow Australian star Russell Crowe. Russell was accompanied by wife Danielle Spencer to the service.
Antonia and Nicole's mother Janelle, who earlier this year celebrated her 50th wedding anniversary with their father, blew a kiss to the car as the hearse departed.
Russell Crowe arrived to pay his respects with his wife Danielle Spencer
His widow had given her own tribute to the man she described as "my soulmate" and "a dear good man". Janelle spoke of his "zest and enthusiasm for life".
"He had a helpless infectious laughter – whether it was a Charlie Chaplin movie or the Road Runner – when Anthony laughed you laughed with him.
"And of course he sang at home at work in his car – he practised in the front porch. "He was persistent setting up of the health psychology unit. I could go on....
"He was a dear good man who will never be forgotten, he leaves behind a family who will be better for knowing him."