In the original documentary, Theroux questioned Leeds-born Savile about the rumours he was a paedophile, which were rejected by the former Top Of The Pops presenter.
Despite spending three months with the prolific sex offender, Theroux failed to expose his sexual abuse and went on to maintain a friendship with Savile between 1999 and 2004, even staying on occasion at the former Jim'll Fix It presenter's house.
In the new film, the 45-year-old documentary maker will revisit his subject to try to "understand the truth more fully" by talking to Savile's victims, friends and family, including those he was introduced to by the radio host.
The BBC has said that Theroux will investigate "how someone he once called a friend used his celebrity status to commit these crimes" and how his public image afforded him immunity.
He will also explore the impact Savile's crimes had on his victims and how he escaped justice for so long.
In October 2012, a year after his death at 84, an ITV documentary called The Other Side of Jimmy Savile broke the seal on the sexual abuse scandal.
The full extent of his crimes was revealed with Operation Yewtree's 2013 report recording 214 criminal offences committed by the star and a further Department of Health report finding he committed sexual attacks at 28 NHS hospitals.
In comments on comedian Richard Herring's Leicester Square Theatre podcast in July this year, Theroux said: "I have grappled with, as someone who made a documentary about him, spent 10 days with him and failed to reveal the fact that he was one of the most prolific sex offenders of modern times possibly.
"I feel a sense of responsibility. I'm trying to go back and figure out how did I miss that?"
Kim Shillinglaw, controller of BBC Two and BBC Four, said: "BBC Two should be part of the national conversation and this challenging subject matter is the kind I want to see on the channel.
"Louis Theroux is one of the country's most talented filmmakers, and I am very pleased that he is revisiting this important - and deeply personal - subject for us, asking difficult questions about the life of Jimmy Savile and those around him and exploring the impact his crimes had on his victims."
Louis Theroux has made many highly acclaimed documentaries for BBC Two, with recent highlights including The Most Hated Family In America, Transgender Kids and By Reason Of Insanity.
His new documentary on Jimmy Savile will air on the channel next year.