The march and rally in the city centre coincided with other marches scheduled to take place in London and Cardiff on Saturday to mark UN anti-racism day.
Organisers of the Stand Up To Racism event said it was aimed at opposing racism, fascism, Islamophobia and anti-Semitism.
Patrick Harvie MSP, co-convener of the Scottish Greens, was among those supporting the event.
He said: “Europe faces its biggest refugee crisis since the Second World War, and some of the responses have been shocking. There are those who seem happy to allow desperate people to drown in the Mediterranean and we see fences and walls being put up to deny fellow human beings safety.
“By contrast, here in Scotland, we have seen an outpouring of compassion from people saying refugees are welcome. On this international day against racism, Scottish Greens stand with others who believe in the principle of free movement of people, and who believe there is no place for discrimination in our society.”
Another MSP backing the campaign was SNP local government minister Marco Biagi, who tweeted: “No to racism; Scotland welcomes refugees.”
Protesters marched in the city centre before gathering for a rally and speeches at George Square.
They held placards bearing slogans such as: No To Racism; No Detention, No Destitution, No Deportation; and Refugees Are Welcome Here.
Lawyer and human rights campaigners Aamer Anwar said thousands attended the event.
He wrote on Twitter: “5,000 march through our city of Glasgow against racism, fascism, anti-semitism, in support of refugees.”
Speaking ahead of the event, Gary Christie of the Scottish Refugee Council said: “This year we have witnessed ever greater numbers of people fleeing for their lives in pursuit of protection.
“The response in Scotland to this has been overwhelming. Thousands of people from all walks of life took to the streets across Scotland to offer solidarity to refugees fleeing Syria. Yet, across Europe we have seen increasing negative political rhetoric towards refugees.
“Scotland can be a beacon for the rest of the UK and Europe in how to welcome and treat refugees.”
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