With Fletcher at the helm, production is expected to resume next week.
There are only a few weeks left on the shoot, which Fletcher will now oversee and then guide the film through post-production.
Bohemian Rhapsody remains on track for a Christmas 2018 release.
Singer was sacked Monday for what a source close to 20th Century Fox told ABC News was a pattern of unreliable behavior on the set.
Explaining his disappearance, the filmmaker's representatives claimed he has been dealing with a health issue concerning his mother. Those reps also argued Singer had patched things up with Malek. Fletcher has appeared in such films as Lock, Stock and Two Smoking Barrels (1998), Kick-Ass (2010) and Stardust (2007). Vaughn produced Eddie the Eagle for Fox.
When Ron Howard famously took the reins of Lucasfilm's Han Solo film after original directors Chris Miller and Phil Lord were fired earlier this year, he reshot large chunks of the film under the supervision of the studio - he effectively made it his own. But the job didn't appeal to everyone. At the time, Ben Whishaw was in talks to portray Freddie Mercury after Sacha Baron Cohen, another actor speculated to star and even write and direct, had walked away at some point in the process. That didn't happen when films like World War Z and the Star Wars spinoff Rogue One had reshoots supervised by others.