Its fairly straightforward, you just have to be organised. First thing to do is de-register from the canton of BS which you can do online. They send you a statement, together with a CHF 20 orange payment slip. You take the statement to the
Gemeinde of wherever you decide to settle in BL, together with your current permit. A few weeks later you should get your new BL permit, so you're now legally resident and registered in BL. If you have a BS registered car, its easy to get BL plates. Just take the BS ones off the car and hand them in at the Motorfahrzeugkontrolle in Füllinsdorf, They will send them back to Basel Stadt for you and issue you with new BL ones.
Your company HR will probably want a scan of your new permit, which will also probably trigger Payroll to adjust your witholding tax. The only major hassle is having to do two tax returns for BS and BL for the year you moved.
The good news is, you'll probably never want to move back to BS