Just adding to what other experts have just mentioned - If your databases are bigger than 500 GB then you can go for Sharding ( SQL Azure DB (PaaS). Otherwise , you can create SQL on Azure VM (IaaS) and host your databases.
There are pros and cons for both the scenario ->
For PaaS -> you can get auto scale up/down scenario along with Scale out through Sharding. Microsoft will manage lots of your operations e.g. backups / SQL health / SQL Availability etc. as mentioned under the posts under
http://dbcouncil.net/sql-azure-db-paas-for-a-dba/
But here , you may need to invest little bit on application code change/development as well.
For IaaS -> You will get the same environment as you get in on-premise SQL server. You will need to manage SQL end to end e.g. Backups/HA/upgrades etc. The database which can create can far bigger because you can also use storage spaces to
make bigger LUNS and create your DB there.
For information on SQL PaaS , you can visit this series -
http://dbcouncil.net/sql-azure-db-paas-for-a-dba/