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Brophy is in his third season at Swindon Town following his 2015 move from Edgware Town.
The 23-year-old, who can play at left-back or left wing, has played 62 games in the league for Swindon so far, including four this season, but following the additions of Kellan Gordon, Donal McDermott, Paul Mullin and Kaiyne Woolery this summer, he has been restricted to appearances off the bench.
He will join a Swindon contingent at Orient as ex-player and manager Martin Ling is their director of football and Jamie Sendles-White signed for the O's this summer following his Swindon release.
Ling worked with Brophy during his short spell as Town boss, which was tragically cut short.
Brophy is the fourth Town man to leave the club on loan this summer, as Will Henry has gone to Dunstable, Jake Evans is at Farnborough and Scott Twine is with Chippenham.
Brophy's contract is up next summer.
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