It was the first senior coaching role for the former West Tigers full-back whose departure was stated by the club to be by 'mutual consent'.
Hull lost only won of their first seven games under the 44-year-old Australian but trailed away to finish a disappointing eighth in the 12-team competition.
This season Saturday's humiliating 36-4 derby defeat by injury-hit rivals Hull KR condemned the black-and-whites to a ninth-place finish.
Hull chairman Adam Pearson said: "On behalf of the board, staff and supporters of Hull FC, I would like to thank Brett for the commitment and dignity he has demonstrated during his two years with the club.
"Brett joined us during a period of transition and the disruption caused by COVID--19, as well as facing further challenges presented by injuries and suspensions.
"The process of appointing a new head coach is underway, with a focused shortlist to identify right person to get the best out of our senior squad, but also someone who will continue to embrace our long-term strategy from grassroots to first team.
Hodgson enjoyed a stellar playing career as a full-back in Campbelltown, playing for both Western Suburbs and Wests Tigers, with whom he won the 2005 NRL premiership, either side of four years with Parramatta Eels.
He then played in Super League for Huddersfield, where he won the 2009 Man of Steel Award, and Warrington, with whom he won both the Challenge Cup and the Lance Todd Trophy.
Hodson had been working with Wests Tigers as an assistant coach, doubling up as Western Suburbs Magpies head coach, when he got the call from Hull in late 2020.
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