Chancellor Angela Merkel hailed him as a "political institution" in Germany.
He is seen as one of the most popular German leaders since WWII.
Mr Schmidt died on Tuesday afternoon in his home city of Hamburg, his doctor Heiner Greten was quoted as saying by German media.
The doctor provided no further details.
Obituary: West Germany's master of realpolitik
In a televised tribute, Ms Merkel said her predecessor was an authority "whose advice and judgement meant something to me".
She said Germans had developed a "deep affection" for him and were "impressed by his personal humility as well as his sense of duty".
Reacting to the news, European Parliament President Martin Schulz said he was "deeply affected" by the death.
"He was an outstanding chancellor, his death marks a turning point for Germany and Europe," he said.
European Commission President Jean-Claude Juncker said Mr Schmidt was "a special man whose political courage has moved many."
Paying tribute to Mr Schmidt, French President Francois Hollande described him as "a great European".
"He was a man who, until his final breath, knew how to give a speech and especially to tell Germans that they had a role to play... that it was within Europe that they should act", Mr Hollande said.
Helmut Schmidt was a far-sighted strategist who lived to see his ambitions for Germany fulfilled in 1990, the BBC's Jenny Hill in Berlin reports.
By 1972, Mr Schmidt was finance minister in the government of Willy Brandt, a brilliant manager of the economic miracle. Two years later he himself was chancellor.
The Berlin Wall dividing West and East Germany was the front line in a dangerous Cold War at the time.
With skilled diplomacy, Mr Schmidt pursued detente with communist leaders on the other side, but when the Soviet Union stepped up the arms race, he stood firm, our correspondent says.
Braving fierce protests at home, he let America deploy medium-range nuclear missiles on West German soil to keep the military balance.