Police estimated that a crowd of about 1,500 walked from the city centre to the Scottish Parliament.
They waved EU and Scottish flags and carried placards showing their opposition to Brexit.
Organisers said the march marked the 60th anniversary of the signing of the Treaty of Rome, which paved the way for the European Union.
It was one of a series of similar events in cities across Europe, including Berlin, Rome and London.
Among those giving speeches in Edinburgh were Green MSP Ross Greer, Alex Cole-Hamilton MSP from the Liberal Democrats, SNP MPs Tommy Sheppard and Joanna Cherry.
Young European Movement Edinburgh chairman Jean Francois-Poncet said the march was to protest against Brexit and commemorate 60 years of the European Union.
He said: "We want to raise the issue in British and Scottish people's lives that you have lies in the referendum campaign that people were not held accountable for and, whether you voted Remain or Leave, that is a real issue."
The march comes ahead of the start of Brexit negotiations, when the UK Government triggers Article 50 on Wednesday.
The UK as a whole voted to leave the European Union by 52% to 48% in last year's referendum. Scotland voted by 62% to 38% in favour of the UK remaining in the EU.
Ahead of the march, Vanessa Glynn, the chair of the European Movement in Scotland, said it would show that Scotland opposes Brexit.
She added: "As the Westminster government is driving us off a Brexit cliff, we will say it loud and clear. Not in our name!
"We have not forgotten how far Britain has come since 1973. We have not forgotten the wars and extremism that ruined our continent before Europeans finally decided to unite their forces to create peace and prosperity instead.
"On Sunday the 26th of March the clocks go forward an hour, then they go back 60 years with the triggering of Article 50 on Wednesday the 29th."
Mev Brown, former Scotland Vote Leave spokesman, said he was not sure what impact the protest would have on the negotiations between the UK and the European Union.
He added: "We've had the referendum. We won. We need to move forward and start the negotiations and get the best possible deal for both the EU and the UK."
More than a thousand campaigners have taken part in a march supporting the European Union in Edinburgh.