The happy couple was pictured enjoying a romantic boat trip together before enjoying a swim in the warm Mediterranean Sea.
Unfortunately, Anderson, 48, experienced a nip slip while changing her clothes.
She was dishing some serious side boob.
What's more, The Fall star even flashed her crack while adjusting her swimsuit.
Later, the couple was seen finishing off their day with lunch Al Fresco at a trendy restaurant on the Rocks.
The pair looked very relaxed throughout the day, taking selfies here and there.
Anderson donned a mis-matched bikini for the excursion, donning pink bottoms and a forest green top.
According to reports, Anderson and Morgan, the Oscar-nominated writer behind The Queen and Frost/Nixon, began dating last October.
Morgan separated from his wife of 19 years, Lila Schwarzenberg, shortly before getting together with Anderson. The former couple shares five children together.
Meanwhile, Anderson has been married twice and has three kids. She split with partner of six years Mark Griffiths in 2012.
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