Users on Geneious Prime 2019.1 onwards can connect to cloud BLAST via the Geneious interface. Cloud BLAST is a BLAST server image provided by NCBI and hosted by Amazon Web Services (AWS). You must have your own AWS account with cloud BLAST enabled in order to use it.
To connect to your cloud BLAST implementation from Geneious, go to Tools → Add/Remove Databases → Set Up BLAST Services. Choose Add alternative BLAST server under the Services drop-down menu at the top of the dialog, and enter the address of your AWS instance.
Cloud blast is preconfigured to require web authentication (http://ncbi.github.io/blast-cloud/usage/authentication.html), users should enter their username and password in the Set Up BLAST Services window as shown above.
This link provides instructions for setting up Cloud BLAST. Cloud BLAST includes some of the NCBI databases (see here for a list). You can also upload your own preformatted BLAST databases created with command-line blast+.