The two companies have not disclosed the financial terms of the transaction.
Midwest Paper vice-president Mike Deprey said: "The Midwest Paper management team and I are looking forward to our partnership with IOP.
"We believe IOP's operations‐focused approach will assist us in optimising all aspects of our business to support continued growth and better serve our customers."
Following the transaction, IOP operating principal Dave Mackin will take over the role of a Midwest Paper chairman.
Mackin is also a member of IOP's Board of Operating Principals, which consists of executives that lead businesses in which IOP invests.
For IOP, Midwest Paper is the company's fourth platform investment for its Industrial Opportunity Partners III fund.
JP Morgan Chase Bank and Chemical Bank provided senior debt financing, while Yukon Partners was responsible for subordinated debt.
McDermott Will & Emery acted as the legal representative for IOP.
IOP director Kyle Hood said: "We are excited to partner with the Midwest Paper team. We believe that Midwest Paper has a strong position in the market and an excellent reputation with its customers."
IOP invests in manufacturing and distribution businesses with revenue from $30m to $400m.
Based in Combined Locks, Wisconsin, US, Midwest Paper specializes in paper manufacturing and distribution. It also supplies recycled containerboard used for corrugated packaging and recycled bag products.