New model: observers have noted that Emma shares a striking resemblance with Bruce's ex wife Demi Moore

"Bruce has fallen for Emma big time," a source has said.

"He is in it for the long-term with her.

"He has enjoyed the bachelor lifestyle for a good few years but thinks the time is right to settle down," the source added.

Willis' daughters Tallulah Belle, 14, Scout, 16, and Rumer, 19, have embraced his new girlfriend into their family and Demi, 45, has too - last month she invited the model to a premiere of her film Flawless in New York.