He passed away on Wednesday while on holiday in the south-eastern town of Bad Fuessing, according to the Cologne archdiocese.
A prominent and outspoken conservative voice, Cardinal Meisner opposed plans to construct a large mosque in the Ehrenfeld area of Cologne in 2011.
He also urged Chancellor Angela Merkel to say sorry for criticising the Holy See's handling of the case of a bishop which denied the Holocaust.
Born on Christmas Day in 1933 in the German city Breslau (now part of Poland and named Wroclaw), his family fled to central Germany in 1945, ahead of the Red Army advancing from Russia.
After studying theology in Erfurt, Meisner was ordained in 1962. He served as the archbishop of Cologne between 1989 and 2014, staying in the position five years past the retirement age at the request of Pope Benedict XVI.
A Catholic journalist based in Rome, Hannah Brockhaus reacted on Twitter, saying: "He was considered a leading conservative Catholic figure in Germany. Eternal rest grant unto him, O Lord."