The veteran star of stage and screen - best known for her roles in The Avengers, Game Of Thrones and On Her Majesty’s Secret Service - died aged 82 in September after being diagnosed with cancer.
Dame Diana stars as a nun in psychological thriller Black Narcissus, alongside Gemma Arterton.
Filming on the three-part drama - about a convent of Anglican nuns in the Himalayas who are overcome with sexual desire - was interrupted by the coronavirus epidemic and subsequent lockdown in March this year.
The BBC’s Chief Content Officer Charlotte Moore commended the "herculean efforts" in the editing room that means the drama will be able to be screened.
Based on a novel by Rumer Godden, Black Narcissus was previously made into a film in 1947 starring Deborah Kerr.
The erotic thriller was banned in Ireland but is now considered a masterpiece.
The BBC has also confirmed the popular Mrs Brown’s Boys will return with a new two-part Christmas special, showing Brendan O’Carroll Agnes Brown coming to terms with “the new normal” of the coronavirus pandemic, and life after lockdown.
And a new seasonal special of popular period drama Call The Midwife managed to be made after the first lockdown.
Moore said: "We were so relieved when they sent me a picture of them finishing production.
"With some shows it's been easier than others to get talent and everyone together, and with some shows it's taken a lot of effort. But I sensed a real camaraderie to make this happen."
The BBC has also confirmed new Christmas episodes of sci-fi drama Doctor Who, comedies The Vicar of Dibley, Not Going Out, Motherland, creative contest The Great British Sewing Bee and gameshow The Wall.
However, lockdown and social distancing measures have meant some shows were not possible.
The Strictly Come Dancing Christmas special will be a compilation of highlights, instead of a seasonal dance contest.
Moore added: "It's been a real struggle but I think people have really wanted to make sure these shows could get on air."
Watch: What happened when Diana Rigg stormed off the Game of Thrones set