The 215,000 sq ft tower will be built at Imperial's White City Campus and is expected to be completed in 2019.
It will provide 192 new homes, including 59 set aside for key workers at the college.
The contract award marks the third project on the White City Campus to be undertaken by Laing O'Rourke.
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The firm has nearly completed a 270,000 sq ft Molecular Science Research Hub and 250,000 sq ft Translation and Innovation Hub.
The two interconnected hubs form one of the first major parts of the innovation ecosystem for the College's new campus.
Paul Sheffield, MD of Laing O'Rourke's Europe Hub, said: "We are delighted to be continuing our ongoing relationship with both Imperial College London and Voreda and look forward to delivering a residential building which will create a landmark building for the White City Campus."
The firm is due to be on site in May.
(LM/CD)
