Hi @John O'Reilly ,
in general it's possible to migrate the VMs from on-premises VMWare to Azure.
Please take a look at Azure Migrate for the migration process.
To connect the Azure environment with your on-premises network you can implement an Azure VPN Gateway Site-To-Site connection or if required Azure Express Route:
Tutorial: Create a site-to-site VPN connection in the Azure portal
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Regards
Andreas Baumgarten