The first contract, a two-stage design and build contract worth £104m, is to upgrade 10 miles of the M62 between Warrington (J10) and Manchester (J12).
BMJV, supported by design partners WSP and AECOM, started design work last month, with works planned to start on site from spring 2018.
It second contract, worth £218m, will see the M27 between junctions 4 and 11 converted to create permanent dual 4-lane all lane running along the 15-mile stretch.
Consultants SWECO/Mott Macdonald and WSP have just started the design work with construction now due to begin in the spring.
Paul Gott, managing director of Highways at Morgan Sindall, said: “These contracts mark the start of two more prestigious projects for BMJV.
“The established relationship between our two companies enables us to provide the best possible service to enhance the capacity and reliability of the UK’s strategic road network in order to improve journeys for road users.”