The contract, which went to Hensel Phelps Construction Company, includes the renovation of about 194,000 square feet of an existing six-story tower and work on two other buildings.
The new inpatient facility is expected to support some 30,000 emergency room visits each year.
The contract also calls for a new 25,000-square-foot building for a cafeteria and offices for the medical center.
The plans for the medical center also include an outpatient facility, budgeted at $125 million, not included as part of the Hensel Phelps contract.
The work is set to be completed September 2013.
City News Service contributed to this report.