The 25-year-old former Tottenham Hotspur player, who has one England cap, had faced a maximum two-year ban.
"Jake's suspension at the club has been lifted," the Championship (second tier) club said in a statement.
"And given the circumstances surrounding the matter we will look to support Jake as he continues to recover from what has been a difficult period for him and his family."
Hull said any internal disciplinary measures that might be taken would remain confidential.
The FA regulatory commission said in a heavily redacted written report -- with six pages blacked out -- that Livermore had admitted the anti-doping violation and knew what he was taking.
It said the death of his son Jake Junior, less than 48 hours after Hull had lost the FA Cup final to Arsenal in May 2014, had a devastating effect on the player, his partner and their families.
Livermore was notified on May 13 this year that his urine sample had tested positive after a Premier League match against Crystal Palace on April 25.
Referring to the 'deeply tragic background' of the case, the commission said "substantial and compelling" evidence had been presented to support the player's contention that "his cognitive functions and judgement were severely impaired at the time in question."
Reaching a verdict of 'no significant fault or negligence', the commission said that "in the circumstances it would be unconscionable to impose any period of suspension."
It directed Livermore to undertake a course of rehabilitation and education, tailored to complement ongoing counselling and treatment, as well as being subject to Target Testing for a year.
Hull were relegated from the Premier League at the end of last season.
(Reporting by Alan Baldwin, editing by Martyn Herman)
Share
