Lasting over seven hours, the memorial was both mournful and celebratory, with the crowd breaking into a spontaneous dance of praise at one point.
Focusing on Franklin's gospel roots, the service featured music from Ariana Grande and Chaka Khan, with Stevie Wonder delivering an emotional finale.
Franklin died earlier this month of pancreatic cancer at the age of 76.
Her final send-off involved 100 pink Cadillacs, a gold-plated coffin, three presidential tributes and eulogies by more than a dozen preachers.
They remembered her not just as the Queen of Soul, but as an aunt, grandmother, friend, civil rights activist and icon of black womanhood.
"The reason that we are here today is because of love. Because of how much we love this woman," said Stevie Wonder, who led the congregation in a rendition of his song As, which carries the refrain: "I'll be loving you always".
"One of my longest friends has gone home," added Motown star Smokey Robinson, who grew up with Franklin in Detroit.
"You're going to be one of the future voices in the choir of angels," he added, before breaking into an a capella rendition of his ballad Really Gonna Miss You.
"Aretha will be influencing others literally for centuries to come," said record label boss Clive Davis, who praised her "once-in-a-lifetime voice".
Pop star Ariana Grande sang one Franklin's signature songs (You Make Me Feel Like) A Natural Woman but elsewhere, the service was like a Who's Who of gospel with powerful and uplifting performances from The Williams Brothers, Vanessa Bell Armstrong and The Clark Sisters.
Jennifer Hudson's stirring rendition of Amazing Grace; and Gladys Knight's version of You'll Never Walk Alone, in particular, drew mourners to their feet, with others raising their arms in praise.
Franklin's son Edward also sang Marvin Gaye's Mercy, Mercy Me; while her niece Cristal remembered the aunt who "taught me bad shopping habits" and "chartered a bus so our family could go to President Obama's inauguration".
Obama was unable to attend the funeral, but sent a speech to be read to the mourners.
"Through her voice, her own voice, Aretha lifted those of millions empowering and inspiring the vulnerable, the downtrodden, and everyone who may have just needed a little love," read his message.
George W Bush also sent a letter to Franklin's family; while Bill Clinton spoke from the pulpit, describing himself as an "Aretha Franklin groupie" and praising the star's work ethic.
"Yeah, she had the voice of a generation, maybe the voice of the century... but she also worked for years when nobody was paying particular attention."
"She lived with courage - not without fear but overcoming her fears.
"She lived with faith - not without failure but overcoming her failures.
"She lived with power - not without weakness, but overcoming her weaknesses.
"I just loved her."
Franklin's contribution to the civil rights movement - both spiritual and financial - was honoured by Rev. Al Sharpton, who said: "She represented the best in our community and she fought for our community until the end.
"She gave us pride and she gave us a regal bar to reach. And that's why we're all here. We don't all agree on everything but we agree on Aretha."
He went on to criticise President Trump, whose initial tribute to Franklin two weeks ago said, "she worked for me on numerous occasions".
"No, she used to perform for you," scolded the pastor. "Aretha never took orders from nobody but God."
At the funeral: Nada Tawfik, BBC North America reporter
Image copyrightGETTY IMAGES
Outside of the Greater Grace Temple, there is an outpouring of love for the Queen of Soul.
Aretha Franklin fans lined up hours before sunrise to get one of the 1,000 seats open to the public for her star-studded funeral.
Many said that they never met her, but knew her intimately through her songs.
Her music continues to move this city, people on the street, in their cars and in their homes have been playing and singing her songs loudly.
In her 1985 hit single, "Freeway of Love," Aretha Franklin sang about cruising around in a pink Cadillac.
In her honour, the streets here were filled with more than 140 pink Cadillacs that will be part of the funeral procession.
Dignitaries and legends may be attending her funeral, but it is the overwhelming admiration and gratitude of the public that underlines her impact on America.
Earlier this week, Franklin's body lay in state at the Charles H Wright Museum of African American History - where she was dressed in a new outfit every day.
For the funeral, she was clad in a sparkling full-length gold dress with sequined heels.
Her body arrived at the Greater Grace Temple on Friday morning in the same white Cadillac that carried her father, Rev. CL Franklin in 1984; as well as civil rights activist Rosa Parks in 2005.
The singer will be buried in a 24-carat, gold-plated casket made of solid bronze.
The interior is finished with champagne velvet, and stitched with her name and her title, "Queen of Soul", in gold metallic thread.
The funeral followed a tribute concert, starring The Four Tops, Angie Stone and Regina Belle on Thursday evening.
Speaking during the memorial service, Detroit Mayor Mike Duggan announced the concert's riverside venue, Chene Park, would be renamed Aretha Franklin Park, so that "performers from generations to come" would be "reminded they are performing at the home of the Queen of Soul".
In a musical career spanning seven decades, Franklin won 18 Grammys, and had 17 Top Ten US chart hits.
She gave her final performance last November at a gala in New York held in aid of the Elton John Aids Foundation.
In his speech, Robinson said the star would never be forgotten.
"The world is celebrating you," he said. "The world is mourning you. The world is going to miss you."