On the watch, go to Settings > General > Reset > Erase All Content and Settings.
Then follow the instructions--ie.e you might need to enter your watch's passcode or Apple ID password. If your watch is a cellular mode, you are asked to keep or remove your cell plan--if nothing changed (same carrier) choose to keep the plan.
After answering any of these things, choose to Erase All. That reset's your watch back to its factory settings. It won't create a backup of your watch's data, so you'll likely lose some data when you pair the watch to your new iPhone.
When you pair the watch to your new iPhone, you need to enter your Apple ID and password associated to turn off Activation Lock and allow the watch to pair to your new iPhone.
That should work. If not, on your new iPhone open Settings > Apple ID then scroll down to the list of devices associated with your Apple ID. Select your Apple Watch and choose to Remove from Account to turn off activation lock. You can also do this via the iCloud website's FInd My and choose to Erase Apple Watch.
Good luck!