According to a comment on Four Weddings and a Funeral costume designer Salvador Perez's Instagram post, the Hulu series will be premiering this June. They have been shooting in London since the end of November, with Tom playing the character Quentin Adams. The series is slated for 12 episodes.

 

Salvador Perez Instagram Post

 

No word whatsoever on the Watchmen premiere yet, although Game of Thrones will start its 6 episode season on April 14th, so presumably Watchmen will be sometime after that.