The instalment, which will air in 2013, is currently filming in Cardiff and will star new Who companion Jenna-Louise Coleman, Doctor Who Magazine reports.
Cross created hit Idris Elba crime drama Luther in 2010 and also served as head writer on Spooks between 2006 and 2008. He is also developing ten-part pirate series Crossbones for NBC.
Mark Gatiss has also confirmed to Digital Spy that he will write a 2013 episode of Doctor Who.
"It's for the new companion, Jenna-Louise Coleman - that's all I can tell you or I will actually be shot!" he joked.
Coleman will first appear in the show's 2012 Christmas special, which will start filming later in the year.
Doctor Who showrunner Steven Moffat recently told DS that he is keen to keep the identity of Coleman's character a secret until Christmas.
"We can't really contain everything, because people will crawl all over us with cameras and sneak views of scripts and call-sheets," he admitted. "Something will get out. But we've been fairly sly, so let's wait and see."
Doctor Who will return to BBC One in the autumn, with the series seven premiere debuting at this year's Edinburgh International Television Festival.
Issue 448 of Doctor Who Magazine is on sale from Thursday, priced £4.50.
> Doctor Who: BBC sci-fi drama moves to new Wales studio - video