Mr Aylwin, a centre-right Christian Democrat, became president in 1990 and oversaw the transition to democracy following 17 years of military rule under Gen Augusto Pinochet.
He was key in setting up a commission which investigated human rights abuses committed during the Pinochet era.
The Chilean government has declared three days of official mourning.
Officials said Mr Aylwin would be given a state funeral.
Patricio Aylwin will be best remembered as a critic of the Pinochet regime and for leading Chile back to democracy, but in 1973, when Pinochet seized power in a military coup, he saw things rather differently.
He initially praised the armed forces for "saving the country from descending either into civil war or Communist tyranny".
But as the 1973-1990 dictatorship wore on and Gen Pinochet showed no sign of stepping down, Mr Aylwin emerged as one of the regime's leading critics.
In 1988 Pinochet called a plebiscite, asking Chileans if they wanted him for another eight years.
Mr Aylwin led the "no" campaign, which won against the odds.
Gen Pinochet quit and Mr Aylwin won the first post-dictatorship election. He assumed power in a tense handover ceremony on 11 March, 1990.
As president, arguably his greatest achievement was to set up the Rettig Commission, which investigated human rights abuses from the dictatorship era.
The commission had to tread carefully - the military was still a powerful force.
But under a mandate from Mr Aylwin, it drew up a comprehensive list of names of thousands of people who were kidnapped, tortured and killed during the Pinochet years.
The former president of Chile, Patricio Aylwin, has died aged 97 of natural causes, his family says.