The contractor will be working alongside two other firms to construct 30 primary schools over a four-year period.
The work is part of the council’s wider £850m primary schools modernisation programme, which will ultimately see all 124 of the area’s primary schools rebuilt by 2016.
Morgan Sindall worked on the earlier phases of the South Lanarkshire primary schools modernisation programme.
It has completed nine schools through the programme so far and is currently on site with four others.
Paul Smith, chief executive of Morgan Sindall Group, said: “This latest framework appointment is testament to the track record we have developed in the Scottish education market.”