Dreher made his professional debut with Palace in a Premier League game against Bournemouth at the end of 2019/20. He was named Under-18 Player of the Season in 2016 a month after making the first-team bench against Manchester United.
He joins Bromley as they sit fourth in the National League under the management of former Academy graduate Andy Woodman.
Commenting on his move, Dreher said: “I’m delighted to have this chance to play competitive football and get back onto the pitch again. I’ve worked hard over the last few seasons and am determined to develop further through this opportunity.”