US Weekly reporting that the child has now arrived. The baby is Michelle's second child, as she is mum to daughter Matilda, 14, from her previous relationship with the late Heath Ledger.
The pair are a Hollywood power couple if ever we've seen one, as Kail directed Williams in the drama Fosse/Verdon, for which she won the Emmy Award for lead actress.
It's reported that the couple met on the drama which Thomas directed and produced - but reports claim claimed that 14-year-old Matilda played matchmaker.
Michelle and Thomas - who directed Broadway hit Hamilton - went public with their relationship at the Golden Globes and Screen Actors Guild Awards ceremonies earlier this year.