Framing Britney Spears featured archive clips of Timberlake discussing his sexual relationship with the singer.
In a statement on Instagram on Friday, Timberlake said he was “deeply sorry” and wanted to “take accountability”.
He also apologised to Janet Jackson, after failing to support her over their controversial Super Bowl performance.
Timberlake and Spears dated between 1999 and 2002, while he was a member of boy band N*Sync.
After their split, he indirectly accused her of cheating on him when he hired a lookalike actress to appear in the video for his single Cry Me A River.
After finding fame at the end of the 1990s, Spears said she was waiting until she was married to lose her virginity.
But during a radio interview, a clip of which features in the documentary, Timberlake publicly revealed that they had slept together.
Two years later, at the 2004 Super Bowl, Timberlake performed with Janet Jackson, accidentally exposing her breast. The “wardrobe malfunction”, as it became known, led to outcry and complaints from viewers.
Although both apologised, Jackson absorbed the bulk of the negative publicity. She was fined and blacklisted by US radio and MTV, and Timberlake’s failure to publicly support her was heavily criticised in later years.
Interest in Spears has been renewed by the release of the New York Times documentary, which examines how Spears has been treated throughout her career.
It has led to criticism of Timberlake and other figures including journalist Diane Sawyer, who told Spears during a 2003 interview she had “disappointed a lot of mothers”, and gossip blogger Perez Hilton, who was involved in the coverage of her 2007 breakdown.
The film also goes into detail about the singer’s conservatorship, a legal arrangement that has given her father Jamie Spears control over her career and financial affairs since 2008.
However on Thursday, a judge upheld a previous ruling that made a financial company a co-conservator for the singer, and rejected Mr Spears’ request to keep his previous level of power over his daughter’s investments. (Courtesy BBC)