In an official statement on the CMVM, Benfica announced that on top of the €68m a further €3.6m in add-ons could follow. In total, Benfica can earn €71.6m (£65.3m) for Dias.
Dias, 23, is one of the most highly-rated young defenders in Europe, a reputation his price-tag reflects.
A graduate of the Benfica academy, Dias made his first-team debut in September 2017 and quickly impressed.
Since then, the 19-time Portugal international has gone on to make 137 appearances for Benfica.
The signing of Dias ends Pep Guardiola’s pursuit of a high-level centre-back, which saw them try to sign Kalidou Koulibaly at first.
When Koulibaly proved too difficult to sign, the Citizens made a bid for Sevilla talent Jules Kounde.
Sevilla rejected City’s bid which led to the English club rekindling their interest in Dias and quickly striking a deal.