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 as shown in the screenshot (replace x's in the location URL with your actual AWS server address and add /cgi-bin to the end of the url).
Cloud blast is preconfigured to require web authentication (http://ncbi.github.io/blast-cloud/usage/authentication.html), users should use "blast" as the username, and their instance ID as the password in the Set Up BLAST Services window as shown above.
You will then need to add the databases you wish to use. Cloud BLAST includes some of the NCBI databases (see here for a list). To add these, go to Tools-Add/Remove Databases-Add Blast database, and select the alternative BLAST server tab. The database name should be written exactly as shown in the table here (see screenshot below for an example).
You can also upload your own preformatted BLAST databases created with command-line blast+.
This link provides further instructions for setting up Cloud BLAST.