According to Scottish Sun, Hibernian accepted a £150,000 (R2,6 million) bid from the Clever Boys for the 26-year-old striker.
Murray hit the back of the net six times in 22 league games for Hibernan last season.
However, they decided to loan him out to Scottish Premiership side Dundee FC in the second round.
The well-travelled marksman managed to score three times in 14 league appearances and he attracted interest from Wits.
This was confirmed by Hibernian manager Neil Lennon, who explained why the club opted against keeping Murray ahead of the new 2018/19 campaign.
The Northern Irish tactician stated that Murray would have struggled for regular game time at the Easter Road-based side.
“I didn’t feel Simon would play that much – he wasn’t really at the forefront of our minds in terms of how we want to play this season,” Lennon told Edinburgh News.
“We brought him in for nothing. We got a good offer for him which we feel is beneficial for the club and him,” he continued.
“He realises he’d have found it difficult to get a regular spot. He quite fancies the challenge of playing in a different environment and culture and financially. I think it’s quite rewarding for him as well,” concluded Lennon.
Murray will reportedly join his Clever Boys team-mates in Johannesburg this week as the team continues its pre-season preparations ahead of the new PSL campaign.
The former Abroath FC and Montrose FC striker will fill the void left by English marksman James Keene at the Braamfontein-based side.
Keene recently joined Wits' PSL rivals SuperSport United on a free transfer after the Clever Boys decided against extending his contract.