The Glasgow giants have been chasing the winger this summer and negotiations took place between Rangers and Schalke over the weekend.
A deal is in place between the two clubs and Matondo travelled to the United Kingdom ahead of completing the move to Ibrox.
According to German broadcaster Sport1, the winger underwent a medical in Manchester with a medical team from Rangers overseeing the process.
Matondo has also given his approval to the move and personal terms over a contract have also been agreed.
Rangers are now on the final stretch of getting the deal over the line before confirming his signature.
The legal teams are finalising the paperwork and once everything is in place an announcement will be made.
Giovanni van Bronckhorst has been keen to add more creativity to his squad in order to compete for the title with Celtic next season.
The Rangers boss will be hopeful that Matondo will add goals and ingenuity in the final third for his side once the deal is over the line.
