Architects Massimiliano and Doriana Fuksas designed the cultural complex for a site in the city's Rhike Park. The project has been ongoing since 2010 and is scheduled to complete later in 2017 when work on the interiors is finished.
The €40 million (£35 million) building comprises a pair of flared, tubular structures clad in a tessellated pattern of steel and glass panels.
One section of its V-shaped plan points towards the nearby Peace Bridge, which was design by Italian architect Michele de Lucchi and completed in 2010.
The Rhike Park is also within sight of the Tbilisi Public Service Hall – an office building sheltered beneath mushrooming steel canopies that Studio Fuksas completed on the opposite bank of the Kura river in 2012.
An exhibition hall is contained in the southern section of the Tbilisi Music Theatre and Concert Hall, which is entered via a set of steps that ascend into a void facing the park.
At the rear of the site, the two volumes connect where they meet an existing 13-metre-high retaining wall.
The rooflines at this end merge and accommodate an alternative entrance from a main road that separates the park from the Presidential Palace.
The structure to the north houses the 566-seat Musical Theatre Hall, along with a foyer and other amenities including offices, storage and technical areas for theatre machinery.
This part of the building is raised up to provide a view across the river through a fully glazed curtain wall from the foyer and cafeteria inside.
"It is a periscope to the city and looks towards the river framing the historic core of the Old Tbilisi," said the studio.
The building's fluid shape is typical of Studio Fuksas's output and evokes previous projects including a school for hotel management in Montpellier with triangular windows punched into its curving facades and an airport terminal in Shenzhen with thousands of hexagonal skylights punctuating its tunnel-like forms.