The 23-year-old attacker was surprisingly sold to the Chilli Boys by Pirates two months ago following a successful season-long loan spell at Baroka FC.
However, Motupa has now been purchased by Wits from Chippa having not even played a single official match for the Chilli Boys.
This was confirmed by the player's agent Abbie Rasimphi of Liberate Resources Sports Management.
"He has signed a four-year deal with Wits. The deal was struck easily because Wits approached Chippa and Chippa agreed to sell the player," Rasimphi told SowetanLive.
The player business manager feels that Motupa will improve at the Braamfontein-based outfit, who won the 2016/17 Premier Soccer League (PSL) title.
"He is very happy. He needs a coach like Gavin Hunt, somebody who pushes players. Now that he'll be under Gavin," he continued.
"He will go places because he will be coached by someone who believes in hard workers. My role was to facilitate and make sure the deal was good for my client," he added.
Wits head coach Gavin Hunt also confirmed the presence of the former South Africa under-23 international.
"He started this morning and it's the first time I saw him today [yesterday]. I do not know what happened between him and Chippa. When he became available we signed him,'' Hunt told the publication.
It is said that the accomplished tactician further revealed the deal did not involve any Wits player moving to Chippa.
Meanwhile, Chippa coach Dan Malesela insisted that he is not disappointed by Motupa's departure.
"It's one of those things that happen in football. I can't say I am disappointed," he said.
"It is better that we lost him before the season starts because we still have time to adjust the squad. Players come and go,'' he concluded.