Mr Barker had been closely involved with the sale until his death in August, Ms Ellison said.
"It was Dad's vision that these businesses would continue to thrive, grow and lead New Zealand's transport industry into the future and we're confident that this sale will ensure this."
Strait Shipping started its Cook Strait service with one ferry in 1992 when Mr Barker wanted a service to transport cattle. It now operates two ferries, the Straitsman and Strait Feronia.
The Barker family will retain ownership of Bulklines and Stocklines, which are not included in the sale.
Sydney-based Champ says it manages about $A3 billion ($NZ3.1 billion) of private equity investments.
Managing director Cameron Buchanan says they want to grow the Barker businesses.
"We're committed to building on the strong foundations the Barker family has created and growing these businesses for the benefit of not only investors but also the wider New Zealand freight and passenger transport markets," he said.
Settlement is expected to take place in the first quarter of 2017 subject to regulatory approval.
Last year Champ bought a majority stake in Christchurch-based outdoor gear chain Macpac.