The former SDLP leader died on Monday, aged 83, following a long illness.
His body was returned to his native city on Tuesday night, ahead of a funeral Mass at St Eugene’s Cathedral.
Mr Hume’s family urged mourners wishing to line the streets to respect Covid-19 guidelines on gatherings and light a “candle for peace” at home.
On Tuesday night, many followed that advice as tributes continued to pour in from presidents and prime ministers for the former SDLP leader.
About 100 people – mostly close family and friends – are expected to attend the funeral service, which has started rt at 11:30 am
Political representatives have begun arriving at the cathedral including Northern Ireland’s First Minister Arlene Foster, Deputy First Minister Michelle O’Neill, Taoiseach (Irish prime minister) Micheál Martin and Irish President Michael D Higgins.