Despite ending their romantic relationship, they're said to remain "great friends".
Anderson, 52, is most well known for her role as FBI agent Dana Scully on The X-Files and as detective Stella Gibson in The Fall. She also starred in Netflix's Sex Education.
She's been praised for her powerful portrayal of Prime Minister Margaret Thatcher in The Crown season 4.
Peter Morgan bagged an Oscar nomination for his 2006 film The Queen starring Helen Mirren. He went on to create The Crown for Netflix.
Representatives for the pair declined to comment to the Daily Mail.
Reports that the pair were in a relationship first broke in October 2016, when it was revealed Anderson was telling her friends about dating the screenwriter.
Anderson, who lives in London, was with Morgan at a party in New York to promote The Crown, where she was heard telling friends that they were in a relationship.
Morgan, whose cinematic claims to fame include Tinker Tailor Soldier Spy and The Queen, was married to Lila Schwarzenberg until 2014, and has five children with her.
Since the relationship came to light, Anderson has been supporting Morgan when The Crown went up for a Golden Globe nomination - and also revealed they were able to work together with an agreement.
"I wasn't allowed to talk with him or express opinions about the scripts, and he wasn't allowed to express opinions about my performance," she told TV Week at the time.
Anderson has daughter Piper, 26, with her ex-husband Clyde Klotz, whom she was married to from 1994-1997. She also has two sons, Oscar, 14, and Felix, 12, with ex-partner Mark Griffiths, whom she dated until 2012.