The company beat a consortium that included engineering firm Mott MacDonald, which worked on the development of a terminal at London's Heathrow airport, and an infrastructure fund backed by former basketball star Earvin "Magic" Johnson.
CNBC reached out to the mayor's office and the Chicago Department of Aviation outside office hours for comments but did not immediately hear back.
Last year, Chicago Mayor Rahm Emanuel called for proposals to design, build, finance, operate and maintain an O'Hare Express operating system through a public-private agreement with the city.
The aim of the project is to cut down the travel time from downtown Chicago to O'Hare International Airport to no more than 20 minutes, according to the mayor's office.
Earlier this year, the mayor's office said that The Boring Company and the consortium, O'Hare Xpress, were shortlisted for the project.
Musk previously said that his company would build a high-speed Loop connecting the international airport to downtown Chicago. When asked to explain what a "high-speed loop" was, and how it was different from a "hyperloop," the tech billionaire explained:
The mayor's office said that each vehicle would carry up to 16 passengers and their luggage, and would depart from O'Hare and downtown Chicago as frequently as every 30 seconds, the Verge reported. It added that The Boring Company planned to charge fares cheaper than what the proposal required: that the premium service should cost less than current taxi and ride-share services.
Emanuel and Boring Company officials said it is too early to provide a timeline for the project's completion or its estimated cost, the Chicago Tribune reported, adding the cost would be born by Musk's company. Negotiations between city officials and The Boring Company would begin to reach a final deal, the Tribune said.
Still, The Boring Company has estimated the project would cost less than $1 billion, the newspaper said, citing a source familiar with the firm's proposal.
Company officials did not immediately respond to CNBC's request for clarification on the project's cost.
The Boring Company started as Musk's idea to build a series of tunnels in Los Angeles to travel underground and let passengers avoid traffic.
The firm raised money by selling company merchandise including hats and flamethrowers. In March, Musk tweeted about a new iteration of merchandise: "LEGO-like interlocking" hollow bricks from the rock beneath Los Angeles, where The Boring Company is tunneling.