Architect Steven Holl has completed a concrete and glass art school at the Museum of Fine Arts in Houston, where students can relax in an outdoor sculpture park and a ramped roof garden.

New York-based firm Steven Holl Architects' Glassell School of Art replaces a 35-year-old building as part of a major redevelopment of the Museum of Fine Arts in Houston (MFAH)'s campus. The scheme was first unveiled in 2015 and also includes an exhibition gallery designed by Holl, and a new conservation centre that are both still under construction.

Holl designed the art school at the northwest corner of the campus to expand the capacities of the MFAH's teaching arm, which was first established in 1927 – three years after the museum opened.

Measuring 93,000 square feet (8,639 square metres), it contains 31 studios for both adults and children to take classes, as well as exhibition spaces, an auditorium, and a series of spaces open to the public including a cafe and gardens.

These facilities are arranged in an L-shape to wrap a central sculpture garden designed by landscape design firm Deborah Nevins & Associates. From this outdoor space, a grass-covered roof slopes up the longer side of the building. It forms a ramp that extends to the top of the three-storey building, which the public can walk up.

Walls comprise sandblasted, pre-cast concrete panels that are punctured by windows in varying shapes – triangles, rhombi and rectangles – to bring natural light into each of the workspaces.

"Our building for the Glassell School is a key part of the overall strategy to shape the public spaces for the entire campus," said Steven Holl in a statement.

"The alternating concrete and glass panels create a porosity between indoors and out, and the gathering spaces – including the building's walkable, sloping roof – provide a civic experience for students and the public alike, with spectacular views of the neighbourhood and the city skyline."

Along with ensuring plenty of daylight, Holl chose concrete and glass to provide a contemporary counterpoint to the neoclassical limestone, and modern steel and glass buildings that populate the museum's campus.

The surrounding site is home to modernist architect Ludwig Mies van der Rohe's Caroline Wiess Law Building, Spanish architect Rafael Moneo's Audrey Jones Beck Building, and the museum itself – designed by Texan architect William Ward Watkin.

A simple palette continues inside Holl's building, where concrete is left exposed and complemented by details of translucent glass – a feature that the architect also used in his luminous Maggie's Centre in London, and an exhibition and performance centre for Virginia Commonwealth University. Fittings in some of the classrooms are also revealed.

Visitors can gather on the amphitheatre-style seating built from concrete in the triple-height forum, placed in the central corner of the school where the two wings meet. The steps are toplit by a large skylight, with the first-floor hallway wrapping around above.

The 75-seat auditorium is located next to the forum, while other areas inside the building include a range of studios for activities like ceramics, jewellery making and fashion design, and a coffee bar.

The Glassell School of Art marks the first stage of the museum's major redevelopment. Holl's Nancy and Rich Kinder Building, which will feature two floors of galleries to display art from the 20th and 21st centuries, and Sarah Campbell Blaffer Foundation Center for Conservation, are expected to be completed in 2020.

Holl – who placed at number 144 on the 2017 Dezeen Hot List of the world's most newsworthy forces in design – is behind the design of several prominent education facilities around the world. One of his best-known projects is the addition to Glasgow School of Art he completed in 2014, but he has also worked on buildings for Columbia University in New York and Princeton University in New Jersey.

Photography is by Richard Barnes.