Pittsburgh-based TMS provides outsourced industrial services to steel mills. It operates 81 customer sites in 12 countries, along with 36 brokerage offices from which it buys and sells raw materials.
The Pritzker family, one of America's wealthiest, operates a global industrial conglomerate and founded the Hyatt chain of hotels.
TMS stockholders will get $17.50 in cash for each share of their TMS Class A and Class B common stock. The price represents a 12 percent premium over the company's Friday closing stock price.
TMS, which went public in 2011, said the deal boosts returns for its shareholders and positions it to expand globally as a privately held company.
The deal, which remains subject to anti-trust approval and other closing conditions, has been approved by TMS' board and is expected to close in the fourth quarter.