The work by the bmJV joint venture will allow traffic to use the hard shoulder between junctions 25 and 30 near Bradford.
The joint venture won a place on the agency’s four-year National Major Projects Framework to deliver Managed Motorways worth £2bn in February 2010.
The price of the M62 job has been reduced by £48m under the government’s cost-cutting drive.
Roads Minister Mike Penning said: “I welcome today’s contract award which confirms that the Highways Agency is on track to start work on this important scheme on time and is making excellent progress against its commitment to reduce the cost of major capital projects by 20% across the roads programme.”
Work on the M62 will include adapting sections of the hard shoulder with resurfacing and drainage improvements for use as either permanent or peak period additional lanes.
The contract is due to start on site in the last quarter of 2011 and to be completed in 2013-14.
Morgan Sindall chief executive Paul Smith said: “This award underlines our strength in the highways sector, where we have an excellent track record and are already delivering a range of projects to modernise the motorway network in the UK.
“It also highlights the value of securing positions on major frameworks, which help to provide visibility and security of earnings.”