Scarlett Johansson moves in with Sean Penn

Scarlett Johansson has reportedly moved in with Sean Penn.

The couple have only been dating since February - two months after 'Iron Man 2' star Scarlett split with ex-husband Ryan Reynolds - but sources say she has already started living at Sean's $3.8 million Malibu home.

An insider told Us Weekly magazine Scarlett "has essentially moved in over the last few weeks," adding that they prefer to " just stay home," rather than be seen in public.

The couple are said to enjoy working out together, eating in and spending time with Sean's children, daughter Dylan, 20, and son Hopper, 17, from his marriage to Robin Wright.

Scarlett, 26, first struck up a friendship with Sean, 50, when she was considering flying to Haiti to help people affected by the two earthquakes in January 2010.

A source explained: "Scarlett first reached out to Sean when she was planning to visit Haiti with Oxfam. She knew Sean was living there in a tent and turned to him for advice."

Although Scarlett wasn't able to make the trip, the couple started dating and made their first public appearance together at the wedding of Reese Witherspoon and Jim Toth last month.