The high-street stalwart has said it will make an equity investment of £33 million and debt investment of £10m into Reiss once the move is completed.
Next added that it hopes its infrastructure capabilities can serve as a "launchpad" for Reiss's growth plans in the UK and overseas.
Lord Simon Wolfson, chief executive of Next, said: "Reiss is an outstanding brand with enormous potential and a first-class management team.
"We are excited to see what can be achieved through the combination of Reiss's exceptional product, marketing and brand building skills with Next's Total Platform infrastructure."
Christos Angelides, Reiss chief executive, said: "I believe the partnership with Next will be transformational for Reiss' operational effectiveness.
"Next's infrastructure will ensure Reiss is not only more efficient as a business, but more effective at serving its customers directly through Reiss stores, at reiss.com and through its worldwide partners."