Mourners and officers stood side by side as the funeral procession set off from Westminster towards Southwark Cathedral.
A floral tribute left on top of the hearse read: "No 1 daddy".
The cortege was led by the Metropolitan Police Colour Party and a "Black Guard" of mounted officers.
Pc Palmer's coffin travelled 2.6 miles along some of the capital's usually bustling streets – but avoiding the scene of last month's atrocity on Westminster Bridge – to arrive for the 2pm ceremony.
In attendance are around 50 members of PC Palmer's family, including his parents and his young daughter.
Thousands of police officers representing every force in England and Wales have turned out to say a final farewell to their colleague.
Met commissioner Cressida Dick – the first female head of Scotland Yard in its 188-year history – is also attending the funeral.
This will be in her first public engagement in her new role.
Police officers protect floral tributes left ahead of PC Palmer's funeral The funeral of PC Keith Palmer – in pictures Mon, April 10, 2017
The funeral of the police officer who lost his life in the Westminster terror attack is scheduled for today at 2pm. His body was transferred to the Palace of Westminster yesterday, where a private memorial service was held for members of his close family
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The hearse carrying the coffin of PC Keith Palmer leaves the Chapel of St Mary Undercroft within the Palace of Westminster
PC Palmer’s coffin was received by the Dean of Southwark, The Very Reverend Andrew Nunn, who also welcomed the congregation.
Prayers will be taken by Reverend Prebendary Jonathan Osborne, Senior Chaplain to the Metropolitan Police Service.
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Chief Inspector Neil Sawyer, who worked with PC Palmer in Bromley Borough and the Territorial Support Group, will then deliver a tribute to the fallen officer.
The service will feature a number of Hymns, including "I heard the voice of Jesus say" written by Horatius Bonar.
PC Keith Palmer's name has been added to the police roll of honour at the National Police Memorial in London.
Floral tributes blanket the street near the site where the PC died
The Commendation and Farewell will be delivered by the Right Reverend Christopher Chessun, The Bishop of Southwark.
At the conclusion of the service, a bugler from the Honourable Artillery Company will play the ‘Last Post’.
The bugler, Lance Corporal Graham Haynes of the Honourable Artillery Company, is also a serving officer within the Parliamentary and Diplomatic Protection Command.
Following this, a private committal will be held.
Yesterday, the officer's coffin was draped in the flag of the Metropolitan Police as it was taken to a chapel just a short distance from where he died.
PC Palmer, 48, rested at St Mary Undercroft in the Palace of Westminster for 24 hours ahead of his funeral today.
The special distinction of a “lying-instate,” normally reserved for senior royals and politicians – went ahead after the Queen gave her consent.
Twelve police officers in full dress uniform formed a guard of honour as eight pall bearers in tail coats brought PC Palmer’s coffin to the chapel.
Four other people were innocently killed and dozens of others injured in the 82-second attack on Wednesday March 22, which ended with lone-wolf attacker Khalid Masood being shot dead.
Officers were told to travel to London in plain clothes
A Metropolitan Police flag flies from Southwark Cathedral