Hi Cristian,
The definitive answer should be:
In the Basic, S0, and S1 service objectives, database files are stored in Azure Standard Storage, which uses hard disk drive (HDD)-based storage media
Source: Here.
For the rest of the tiers apply the following:
Both Standard tiers and Premium tiers use a technology called Azure Premium storage, which is eventually backed by SSD. On Standard tiers, the storage is remote from the SQL Server instance processing user requests. On Premium tiers, the SSD storage is local. There are mainly two benefits. First, latency is sub-ms for local reads compared to muli-ms for reads from XIO. Second, SSD supports higher IO throughput. Best regards.
Source: Here.
Estienne Granet was a Microsoft Employee that was my primary connection with Azure SQL team. He is a very trusted source regarding Azure SQL.