The project, worth €40m (£31m), is scheduled for completion in 2015.
Lublin is Poland's ninth-largest city and one of the country's most important academic and cultural sites. The authorities envision the Cultural Encounter Centre as becoming one of the city's landmarks.
The project requires the partial demolition of a 40-year-old unfinished building and the construction of the new building in its place. The centre will have five floors, two of them underground, and a multifunctional hall accommodating 1,200 people.
As part of this contract, Budimex will also refurbish the adjacent building, which houses the Musical Theatre and the Henryk Wieniawski Lublin Philharmonic, and build a new 5,000m2 plaza and an underground car park.