Celtic are set to receive around £100,000 in compensation for the departure of the highly-rated forward, who moves south after impressing at academy level in Scotland. Rennie was part of Celtic's B team and had also represented Scotland at Under-15 level, catching the eye with his pace, dribbling and eye for goal despite limited senior game time.
The move continues a pattern of Fulham targeting some of the brightest teenage talent from around Britain and Europe as part of the club's long-term recruitment strategy under head coach Alvaro Arbeloa.
Rennie is understood to have picked the west London club ahead of interest from several other sides in England and on the continent, with his development pathway cited as a key factor in the decision.
For Celtic, the departure represents another instance of a promising academy graduate moving on before making a first-team impact, following a string of similar exits over the past year.
Dara Jikiemi left for Liverpool this summer after progressing through the Parkhead youth setup, while winger Conall Glancy joined Tottenham Hotspur last August and forward Daniel Cummings signed for West Ham United after his contract expired, having established himself as a regular scorer for Celtic's B team.
Rennie is not expected to be fast-tracked into first-team contention at Fulham and will instead continue his development within the club's academy set-up as he adjusts to English football, with the Cottagers hopeful his early promise can be nurtured into a senior career in the years ahead.
The signing underlines the growing willingness of Premier League clubs to move for teenage prospects north of the border, with Scottish academies increasingly seen as fertile recruiting ground for English sides looking to build for the long term. Rennie's switch is expected to be formally confirmed once the paperwork is finalised in the coming days.