The new all-purpose building is due for completion in the coming weeks, on land at Hunslet Lane and Black Bull Street, in Leeds City Centre.
Mr Baveystock was given a tour of the facility, which he described as "inspiring".
He said: "This new facility will provide an inspiring atmosphere for students of the Leeds College of Building, and that is hugely important. We want to galvanise the enthusiasm of those young people who will go on to form part of the civil engineering workforce of the future.
"With more than half of the space dedicated to specialist workshops, it is heartening to see such a strong emphasis upon the practical, alongside the intellectual and theoretical elements of studies."
Mr Baveystock met management of the College, as well as students.
Ian Billyard, Principal of Leeds College of Building, said: "We have developed excellent links with the Institution of Civil Engineers over recent years, following development of Advanced and Higher Apprenticeships. It was wonderful to host the visit of Nick Baveystock and ICE's Regional Director Penny Marshall, where they met students and staff. We are looking forward to developing our excellent links even further."
The lead contractor on the facility is GB Building Solutions, with AECOM as project managers.
Photo (left to right): Nick Baveystock (Director General, ICE), Penny Marshall (Regional Director, ICE Yorkshire and Humber), Ian Billyard and Mark Wright (Leeds College of Building).