Connectivity between Pokémon HOME and Pokémon GO is planned to be up and running by the end of the year.
This link will let you send Pokémon you’ve caught in Pokémon GO to Pokémon HOME. From there, some of these Pokémon can be brought into Pokémon Sword or Pokémon Shield to join your Galarian adventures.
In order to bring certain Pokémon that were caught in Pokémon GO and then transferred to Pokémon HOME into a Pokémon Sword or Pokémon Shield game, the Pokémon must either be registered in the Pokédex of that game or have been obtained at least once in that game.
When preparing to transfer Pokémon from Pokémon GO to Pokémon HOME, please be aware that you must have completed the tutorial section of the mobile device version of Pokémon HOME. There are some special Pokémon that cannot be sent to Pokémon HOME from Pokémon GO.
Be aware that Pokémon transferred to Pokémon HOME from Pokémon GO cannot be returned to Pokémon GO. Further details on connectivity between these titles will come in future updates. Please visit the Pokémon HOME website for details on other titles that have connectivity with Pokémon HOME.