Reid was appointed at Selhurst Park at the start of the 2017/18 season and played a key part in keeping the Eagles in the Premier League, following an awful start to life under newly appointed manager Frank de Boer.
Nothing had been confirmed by the club throughout the summer, and there was still no news over Reid's future after he was seen to be absent from the touchline in Crystal Palace's opening two games this season.
But ahead of their short trip to Watford on Sunday, Hodgson confirmed that his former colleague had left his position due to personal reasons.
"Yes, unfortunately, he has decided to leave the club to take a break away from football, he has personal issues that he wants to sort out," Hodgson confirmed, quoted by football.london.
"It’s a sad situation for us because we really enjoyed working with him, he did a fantastic job last season and we will miss him, but we have to respect his wishes and only hope the personal issues he has he will be able to resolve."
Crystal palace playing really good football, they are underdogs for Europe this season. quietly effective— Nwikyz (@nwikyernest) August 20, 2018
Crystal Palace have enjoyed a promising start to the new season despite losing their last match against Liverpool, where exciting defender Aaron Wan-Bissaka was sent off mid-way through the second half.
Wilfred Zaha took centre stage for the Eagles on match day one when the club secured a comfortable win over London rivals Fulham, and Palace will be hopeful of registering a similar result at Vicarage Road on Sunday.