Unfortunately, Fitbit doesn't currently support the sync with Apple Health, but you can use other apps to accomplish that.    

For this reason, we took it upon us to develop FitbitSync, an app that automatically syncs all of your Fitbit data to Apple Health.  

If you wish to only sync your steps,  you are good to go with the free version.   
If you want a more complete analysis of how you have been doing and sync much more data, jump on the 7-days free trial of the PRO version!   
FitbitSync PRO allows you to further sync: distance, workouts, sleep analysis, flights climbed, water, active energy and much more!   
With the Auto Sync, your Fitbit Data will automatically be synced to Apple Health.

Please note: Always make sure that both Fitbit and FitbitSync apps are open in the background!

Please contact us via help@steps.app if you need further support in order to connect Fitbit to your device.