The 23-year-old winger has joined on a three-month deal, and is eligible to make his O’s debut this weekend at Aldershot Town.
Born in London, Brophy started his youth career at Harrow Town before signing for Broadfields United in 2013.
Following two years at Broadfields, Brophy then joined Edgware Town where he impressed before attracting interest from Swindon Town where he eventually signed during the summer of 2015 after a successful trial.
Having racked up 31 appearances during his debut season at the County Ground, the winger was handed a new deal ahead of the 2016-17 season.
Brophy made a total of 33 appearances for the Robins last season, scoring his first Swindon goal against Queens Park Rangers in August 2016, and racked up six appearances for David Flitcroft’s side this campaign.