When episode two of the series aired on Channel 4 in December, it featured a range of pre-recorded sketches and Boyle making jokes in front of a studio audience, including derogatory remarks about celebrities such as Jade Goody, Heather Mills, Michael Jackson, Katie Price and Susan Boyle.
Ofcom received around 50 complaints about the programme, including one from Price, who accused Boyle of being a "bully" over comments made about her disabled son Harvey.
Another complainant described the sketches and jokes in the programme as "atrocious, demeaning and degrading... [and] entirely reprehensible".
As Channel 4 made the show available on catch-up platform 4oD, ATVOD, which this week changed its name from the Association for Television On-Demand, was tasked with addressing the complaints.
Statutory rules for VOD content are significantly less strict than those for TV broadcasts, and do not currently prohibit programming that is deemed offensive. In cases where content "might seriously impair the physical, mental or moral development of persons under the age of eighteen", providers must make efforts to prevent young people from accessing the material.
After reviewing Frankie Boyle's Tramadol Nights, ATVOD ruled that the programme would not seriously impair the development of under-18s and so decided not to take any further action. The regulator also noted that Channel 4 had run a warning around the programme on 4oD, despite not being obliged to do so.
Commenting on the decision, ATVOD chair Ruth Evans said: "Many viewers may regard the material as highly offensive, including to people with disabilities, and unsuitable for under-18s, but providing such content to under 18s is not a breach of the rules set by parliament if it does not fall foul of the 'might seriously impair' test."
Ofcom is still conducting its own investigation into whether the original television broadcast was in clear breach of the Broadcasting Code. It will issue a report over the coming months.
Last month, ATVOD proposed increasing the level of regulatory fees for UK video on-demand operators to tackle its budget deficit.