It was reported in the run up to the BBC One series' launch that Simon had instructed lawyers to look over the new show.
There were suggestions that Gary's talent search - hunting for five male singers to form a new band for a musical - would be similar to X Factor and another of Simon's reality shows, La Banda.
"Simon’s team was keeping a close eye on Gary’s show. They want to make sure that it’s completely different to his own projects," a source said at the weekend.
But they revealed to the Sunday People newspaper: “Simon has since been advised to abandon his case against Let It Shine.
“He is very serious when it comes to protecting the intellectual property of his shows. He trailblazed in the TV talent show sector and has to protect his brand.
“But it’s very hard to win these kind of cases and his legal team has gone back to him to say any action would most likely be fruitless.”
While Gary's show is a singing competition the format is rather different to any seen before, with the judges' marking the acts who need to score at least 15 points to get through the auditions.
Gary said last week: “This show is no threat to any of [Simon's] shows. It’s not on in a time period when any of his shows are on."
Saying there was no 'war' between him and Simon, the Take That legend continued: “I’ve always been a big fan of The X Factor and a big fan of Simon as a TV personality, and of the person I’ve met throughout the years
“I’m not very close to him, I never have been, but this show is of no threat to any of his businesses."
Gary went on to point out that Let It Shine was on the hunt for musical performers and not chart toppers.
He told the Daily Mirror newspaper: “My winners will not, I don’t think, be having any recording contracts and will be doing theatre shows.
“As far as I know there is nothing within Simon’s company that has anything to do with theatre. It is of no threat whatsoever, other than me being on TV, that is the only link.”
Let It Shine continues Saturday nights at 7PM on BBC One.