The swap deal comes after Lakay signed a pre-contract with the Students at the start of the year.
Matsatsantsa held meetings with the Braamfontein-based side in order to allow Lakay to move to Johannesburg immediately instead of waiting until the end of the season.
The two teams then reached an agreement with Wits including Macuphu in the deal.
Lakay, however, will spend the remainder of the term on loan at Wits before joining his new teammates on a permanent deal in July.
Moving the other direction is Matsatsantsa forward Fagrie Lakay— SuperSport United FC (@SuperSportFC) January 29, 2019
Lakay signed a pre-contract with the clever boys with effect from 1 July 2019, but will join @BidvestWits immediately #ForeverUnited🔥 pic.twitter.com/sCdG3PbrZQ
Both Macuphu and Lakay will be available immediately for their respective teams.
Macuphu, who joined Wits from Chippa United at the start of the season, managed 14 appearances all competitions and scored twice in the first round of the 2018/19 season.
Lakay, on the other hand, featured in 11 matches for Matsatsantsa this season without finding the back of the net.
This was after he returned from his loan spell with Ajax Cape Town at the start of the current campaign.