Kunis, 28, will spend several months in London filming the film alongside actor Eddie Redmayne.
"Mila is going for at least six months filming near London and Ashton has decided to head here too. They spend most of their time glued to each other's side," a source told thesun.co.uk.
The couple has been spotted house hunting in the upmarket Marylebone area in central London, where their neighbours would include A-listers Kate Hudson and Guy Ritchie.
Meanwhile, Kutcher has some free time as he has wrapped up shooting his Steve Jobs biopic, "jOBS". He is reportedly keen to spend time away from the US, where his divorce to estranged wife Demi Moore is being finalised.