We migrated our on premise TFS to the cloud using third party tools. This was really hard and took us over a year. I’m glad I had not tried this with a customer. The good new is: Microsoft announced this week the availability of the migration service. The service allows you to migrate your projects with a defined process.
The service offers a migration tool that helps you to prepare your projects and do the migration. Under the hood there are two ways the migration works. For small databases it uses a dacpac package. For large databases (>150 GB) you have to restore the database in Azure and the import directly accesses the database.
You can download the migration guide and the migration tool.
There are a few DevOps partners that participated in a boot camp in Redmond and have the skills and resources to help you with the migration. I’m happy that Alegri is one of them. The partners also have access to additional resources and funding from Microsoft – so I advice you to contact one if you plan to move to the cloud.
writeabout.net 
Have you tried the new TFS to VSTS migration process? We have several internal teams that want to migrate so I’m planning on use it. Wanted to know if there was anything outside the documentation that I needed to take into consideration.
The private beta was sadly only for very big companies. I played around with the tooling in the boot camp. But I really advice you to take a partner with good connections to the product group. You can do al lot of work yourself – so you don’t need too much consulting time. And you may get fundings from msft.