People cheered, clapped and threw flowers as the funeral cortege passed by.
The 56-year-old was best known for her 1990 single Nothing Compares 2 U, which catapulted her to worldwide fame.
O’Connor died at her home in London in July.
Irish President Michael D Higgins and his wife Sabina attended the service, as did Taoiseach (Irish Prime Minister) Leo Varadkar.
The cortege was led by a VW camper van, playing music from four large speakers on the roof.
The precession stopped briefly outside the singer’s home, where it was met with a rapturous round of applause.
Bob Marley and the Wailers’ Natural Mystic was played from the camper van.
It is the opening track on the reggae superstar’s landmark 1977 album Exodus, and he was one of O’Connor’s heroes.
In a statement, O’Connor’s family said she “loved living in Bray and the people in it”.
“Sinéad’s voice carried with it an undertone of hope, of finding one’s way home.
A tribute to O’Connor was unveiled on a cliff close to Bray over the weekend with large, white letters spelling out “Éire [Ireland] loves Sinéad”.
It was designed by Dublin-based creative agency The Tenth Man.
‘Today I’m broken’
Maureen Sullivan travelled to Bray from Carlow to pay her respects.
“She spoke out for us all.
‘She is very important to me’
Isabelle Ferrer travelled to Bray from Dijon in France.
“She was my favourite singer ever,” she told BBC News NI outside O’Connor’s former home on Tuesday morning.
“Representing women, she was far ahead of her time, a long ago.”
She has a tattoo of O’Connor’s autograph.
I knew her life. She is very important to me,” she said.
“I think there is something about her soul, something about her.”
‘I wanted to let her know she was loved’
For Pauline Scullion, O’Connor’s music helped her through some of the darkest moments of her life.
She travelled to Bray from Bellaghy, County Londonderry, with her partner Shane Hughes.
“I wanted to let her know that she was loved, respected.
“She meant an awful lot to me.
“I hope that us being here today can sort of show her family how much she meant.”