Tim Willcox was quoted as being "hopelessly in love" with his co-star Sophie Long, according to The Sun.
The 49-year-old father-of-four has reportedly told his wife Sarah about the affair.
He is said to have attended Long's wedding to yacht salesman Will Green in Cornwall in June 2010.
A BBC spokesperson said that the pair will not appear together on screen in the near future, saying: "They are not scheduled to be presenting together, but there is no ban."
A friend of Wilcox is reported to have said: "He is very charming and has lots of female fans but he is also very honourable so all this will have been very difficult for him."
The pair are regularly seen presenting BBC News at different stages of the day.
Tim Willcox was particularly praised for his coverage of the Chilean miners' crisis for the channel in 2010.