The council-backed scheme will last 15 months and is being delivered by Runcorn-based Ashall Property.
Up to 150 construction jobs will be sustained during the conversion of the Grade II listed building, which has been empty for the past 20 years.
Liverpool City Council purchased the freehold of the landmark for £1.95m earlier in 2013, which enabled £18m of private investment to go ahead.
Mayor Anderson said: “The Royal Insurance building has been empty for too long, and its rebirth is great news for our city, for our economy and for our hotel sector. We are protecting our past, as well as investing in our future.“