Due to be completed early next year, construction was launched with a groundbreaking ceremony with principal Jim Grant joined by GFirst LEP chief executive David Owen.
Mr Grant said: "This building will transform the digital education the college can provide, including several of the new T Levels.
"Facilities in the building will enable students and employers to work together on a wide range of projects and provide opportunities to develop adult education. We look forward to its completion next February and being able to welcome employers, students and members of the community to the events we will host there in 2022."
Mr Owen said the project was exciting for the whole of Gloucestershire. He said: "The cyber and digital sectors are moving forward at pace and even as we are coming to the end of lockdown, more employees will look to continue to work from home and adopt blended working patterns, making these sectors even more important for our economy. "We need the next generation of students to be right at the forefront of digital education and this project will enable that to happen."
Thomas Jones, Associate Director at E G Carter & Co Ltd said: "The three-storey digital building designed by Roberts Limbrick will provide a central atrium and flexible spaces with the ability to offer a variety of teaching and learning environments for the college students.
"Over the next few months we will be working together with the college to provide valuable work experience which will help their construction students on their chosen career paths."