The 22-year-old has spent more than a decade with Fulham's academy, having joined the club at under-nine level, but turned down fresh terms in favour of a permanent move away.
Sanderson never made a senior appearance for Fulham's first team despite being promoted into first-team training in 2022, with the past four years instead dominated by a string of loan spells across non-league and the EFL.
The Chichester-born forward has previously represented Oxford City, Sutton United, Bradford City and Harrogate Town during those loan stints, gaining experience across National League and League Two football.
His most productive spell came last season at National League club Woking, where Sanderson scored 19 goals, a return that appears to have convinced Stevenage to move for him on a permanent basis.
Stevenage have signed the striker on a two-year contract, giving him his first senior move away from Fulham since joining the club as a boy.
Fulham confirmed the transfer in a statement praising Sanderson's contribution throughout his time in the academy pathway, while wishing him well for the next stage of his career.
"Olly had his most prolific loan spell last season, scoring 19 goals for Woking," the club said, highlighting the form that ultimately played a role in his departure.
The move represents a fresh start for Sanderson at a club competing in League One, the third tier of English football, where regular first-team football should now be more readily available to him.
For Fulham, Sanderson's exit is part of the natural churn of academy graduates who, despite years of development, do not progress to senior involvement at Premier League level.
His departure also continues a familiar pattern for English academies, where prolific loan spells in the lower leagues often serve as the platform for a permanent switch rather than a route back into a parent club's first-team picture.
Sanderson will now report for pre-season training with Stevenage, who will be hoping his proven goal-scoring record in non-league translates into senior EFL football as they prepare for the upcoming League One campaign.
For a player who spent 14 years at one club without making a first-team appearance, the move to Stevenage offers something Fulham could not: a clear path into a starting eleven.