The 12-month contract includes strengthening, maintenance and refurbishment works on the current bridge.
BAM is due to start this summer strengthening girders, replacing the eastbound carriageway expansion joints and installing new lighting.
The work will mainly take place inside and underneath the bridge.
When finished, the 40mph speed limit, which was established with the narrow lanes in 2007 to reduce the effects of extra weight on the bridge, will also be lifted and the original lane markings reinstated over the viaduct
Transport Minister Stewart Stevenson said: “The M8 is a vital link in our strategic road network, and this bridge is now over 30 years old and requires strengthening to bring it in line with modern standards.
“This section is used by over 80,000 vehicles daily, and once completed these improvements will benefit motorists with a superior, safer route.