When migrating DHCP I like to gradually shorten the lease time until I get all devices renewing their lease daily. Then on Friday night I turn off the old DHCP server and turn on the new one. Monday morning they should all be using the new DHCP server so I gradually turn the lease time back up. Options in DHCP should be pre-configured with the new DNS server, along with reservations and the like when it goes live. The moment you flip the switch, grab a laptop and do a release/renew to make sure it pulls the proper settings from the new server.
For DNS, if the devices can import from AD, then away you go, if not then you may have to enter everything manaully. All hard coded devices(static IP) will have to have the new DNS entries modified, including the edge router, switches, etc... Now would also be a good time to look around for anything using the local hosts files, and straighten that out to.
How complidcated this can get will depend on your particular network, and what kind of shape it is currently in. Good luck .