To copy the files, settings, and OS X user accounts in your backup to another Mac(a new Mac), use Migration Assistant.
https://support.apple.com/en-us/HT204350
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May I ask you if according to your experience the Migration Assistent restores also all the Applications (like Office, Mail, Photoshop and so on)?
I never used it and wonder if it helps avoiding to have to install all the previous software in a new computer.
Since it can (according to Apple) also "migrate" from a PC to a Mac, I can hardly imagine that software (which is also dependent on the OS, wether it is Windows or a different OSX) might be migrated to a new system through this tool.
Users folders, personal documents, music, pictures... I can imagine to be possible, but software ??
Thank you in advance for your answer.
Ed