The couple reportedly bought the luxury property from prolific Shameless creator John Wells, who initially put it on the market for $7.9 million.
Built in 1923, the Mediterranean-style mansion is one of the best of the historic properties in Hancock Park, one of the oldest and most upscale neighbourhoods in Los Angeles.
Many celebrities, including Muhammad Ali, Shonda Rhimes, Antonio Banderas and Melanie Griffith, have lived in this lush setting.
Drew Scott's famous honeymoon house is also nearby, where he and his family currently reside.
But Daddario's home is one of the crown jewels of the area.
The home once belonged to renowned architect William Hefner and renowned interior designer Kazuko Hoshino, whose signature style is still evident.
According to the listing information, the home also has French influences.
The property consists of an elegant main residence and a separate two-storey guesthouse.
High-end materials include limestone, marble slabs and tiles.
Ornate iron and glass detailing can be found in both structures.
The two buildings offer a total of 5 bedrooms and 2.5 bathrooms, with 4,910 square feet of living space.
There is an abundance of natural light, giving the rooms a spacious and airy feel.
The main suite has a fireplace, walk-in wardrobe, French doors, and a spa bath.
The eat-in kitchen has calacatta marble countertops and an island, and a rustic fireplace.
The manicured grounds include olive and sycamore trees, as well as patios, gardens and a 60-foot swimming pool.
A tall hedge at the front provides privacy from prying eyes and paparazzi.
Daddario, 36, achieved her professional breakthrough in the Percy Jackson film series.
Since then, she has been prominent in television series such as White Collar, Parenthood, True Detective and Why Women Kill.
She was nominated for an Emmy for her work on White Lotus and will star in the series Plum Witch, which premieres in 2023.