It depends on your existing Windows 10 license.
If you purchased and installed the full retail version of Windows 10, you can transfer it to a new computer. Either by moving the SSD intact to the new system (it will need to work for a while to setup for the new hardware and, of course, any problems that might have slowed-down or caused unreliability on the old computer will transfer to the new one), or by re-installing from scratch.
If you upgraded to Windows 10 from a full retail version of Windows 7 or Windows 8, you can also transfer your license to a new computer as above.
In both the above scenarios you will need to reactivate Windows 10 manually since, even if you move the SDD intact, it sees enough changes to key hardware components to believe it is being installed on a new PC. This will involve a phone call or chat session with Microsoft to get the new activation key. Usually not a problem unless your key has somehow been pirated.
If your old computer came with an OEM version of Windows 10, or was upgraded from an OEM version of Windows 7/8, you cannot transfer that license to a new computer and will have to buy a new license. You can still move the SDD intact to the new computer, but will need to change the product key.