The work included the refurbishment of period features throughout the building and the addition of new exterior stairs and a lift.
A spokesman said The Tetley is a result of relationships and investment from the private sector, specifically Carlsberg UK which owns the building and has supported its refurbishment.
Chris Walker, divisional director of Esh Construction, said: “This project has seen the extensive renovation of one of Leeds’ most loved buildings and our team are proud of the results.
“The work has created a new cultural space for people of all ages to enjoy.”
The Tetley is managed by Project Space Leeds and is a new contemporary visual arts centre for the city. The capital funding is supported by Arts Council England to help convert the building into gallery and community spaces on ground, first and second floors, alongside further refurbishments to event, retail and cafe areas.
Project Space Leeds will also look after the Tetley archive.
The redevelopment has preserved heritage features such as the original boardroom and war memorials in the building.
Kerry Harker, of Project Space Leeds said: “The Arts Council’s funding, added to the tremendous support we have had from Carlsberg UK, puts us on a more sustainable footing which means that we can focus our efforts on creating a centre of excellence for contemporary visual art.
“We want it to be a first class resource for local people and an important attraction for students and visitors to Leeds.”
Esh Build is part of Esh Construction.