Migrating from one Office 365 tenant to another can seem daunting, but with some planning and patience, it can be accomplished smoothly. Here is a step-by-step guide on how to migrate your data:

1. Take stock of what needs to be moved. Make a list of mailboxes, Sharepoint sites, OneDrive content and any other O365 workloads in use. This will help you plan.
2. Set up your new O365 tenant. Ensure all licensing is in place beforehand so there are no roadblocks during cut over.
3. Use a third-party migration tool. Native tools like Microsoft Migration Tab can work for small amounts of data but are not practical for whole tenants. Commercial Migration Services can automate migration, saving hours of work.
4. Migrate in stages if the data set is large. Rather than risking downtime for users, move department by department. This also lets you test and optimize as you go.
5. Manage DNS cutover carefully. Once DNS routing is changed, mail will start flowing to new tenant so timing and planning are critical.

I hope these tips give you a good starting point for planning your Office 365 migration. Read this guide on tenant to tenant migration for detailed steps and instructions.

Also read: Best OST to PST Converter | Migrate from G Suite to Office 365