The pair would leave Griquas at the end of the Currie Cup season.
Human would take up the position of coach at the University of Pretoria from 2014 which includes the role as head coach for the Varsity Cup side, as well as other competitions such as the Carlton Cup, USSA tournament and the Predator series.
He would replace Nollis Marais and Riaan Vorster as the Varsity Cup coach and the USSA coach, respectively.
After the completion of the Currie Cup competition, Human would join Tuks from November 1 for a three-year stint.
"I thoroughly enjoyed my time at Griquas and wish the union and the players all the best going forward, but I am not getting any younger and I need to take a new opportunity if it arises," Human said on Tuesday.
Minnie would leave Griquas in December to move to George and pursue a business opportunity.
"I spent 11 years in Kimberley and leaving Griquas was a very difficult decision," Minnie said.
"I put a lot of thought into it and, in the end, made a business decision that will work best for me and my family."
The union would advertise the post of head coach within the next few days, hoping to make an appointment by November/December.