The operation was carried out early on Thursday morning, a day after it was announced the monument will be displayed in a museum.
It will stand alongside placards from the demonstration on Sunday sparked by the death of George Floyd, that culminated in a moment that made headlines around the world.
Bristol City Council said the decision to move it to a museum was being taken so “the 300 year story of slavery through to today’s fight for racial equality can be learnt about”.
Bristol Mayor Marvin Rees, added: “The events over the last few days have really highlighted that as a city we all have very different understandings of our past.
“The only way we can work together on our future is by learning the truth of our beginnings, embracing the facts, and sharing those stories with others. This is why this commission is so important.”
What to do with the stone plinth upon which it stood has yet to be decided but the council promised to make a decision “democratically through consultation”.
The memorial to Colston, who made his fortune in the slave trade in the 1600s, had stood in the city since 1895 but in recent years was the subject of a number of petitions – the most recent of which garnered more than 10,000 signatures.
On Sunday protesters took matters into their own hands, tying a rope around the head of the statue and pulling it to the ground.
It was then rolled from the city centre and dumped unceremoniously into Bristol’s harbour – almost exactly at the point where Edward Colston’s ships would have once left for West Africa.
The episode has led to debates in the UK over statues of historical figures who made fortunes and reputations on the exploitation of others.
A statue of slaver Robert Milligan outside the Museum of London Docklands was pulled down on Tuesday and there has been a renewed push for Oxford University to take down a monument to the imperialist Cecil Rhodes.