It was posted a while back that Michael Dougherty would write the Godzilla sequel with Zach Shields, now it has been announced he will direct it as well. He has apparently been working on writing it for a while and now was offered the director's chair. He has worked with Legendary before so he was known to them. Alex Garcia will oversee the project for Legendary. No word on Thomas Tull's involvement.
Godzilla 2 is currently dated for Mar. 22, 2019, with Godzilla vs. Kong set for May 29, 2020.