The 46-year-old will succeed Nicholas Serota in one of the most influential jobs in the country's arts industry after transforming Manchester's cultural landscape.
"I am honoured to be asked by the trustees of Tate to become the new director," said Balshaw, who takes over on June 1.
"Under Nicholas Serota's leadership, Tate has changed forever how we all think about art and artists and has made visual art a central part of a vibrant cultural life in the UK."
Serota has run Tate for almost 30 years, transforming it into a global brand, and is leaving to become chairman of Arts Council England.
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He masterminded the creation of London's Tate Modern, the world's most popular modern art museum, and oversaw the institution's other three galleries: Tate Britain in London, Tate Liverpool and Tate St Ives.
Balshaw will quit as director of the Whitworth Art Gallery in the run down Manchester neighbourhood of Moss Side.
She oversaw its 17 million pounds ($20.6 million, 19.3 million euros) renovation and helped it win Museum of the Year in 2015.
Balshaw earned a reputation as a champion of live and performing art with one installation consisting of an artist spending 65 consecutive days in front of a live audience, eating, sleeping, and drawing.
She has been credited with significantly expanding the collections of the galleries she leads.
"The trustees and I know that Maria has the vision, drive and stature to lead Tate into its next phase of development," said Tate chairman of trustees John Browne. "We enthusiastically look forward to working with her as she does so.