She is to replace Amanda Jones and will join the central London venue on 9 May.
Hyde, who has held a variety of senior PR posts in arts and cultural venues, will lead the four-strong media relations team and report to Barbican MD John Tusa.
'It is quite similar to the role I had at the South Bank although the conference and commercial side is a key feature at the Barbican,' said Hyde.
Hyde joined Sadler's Wells in June 2003. Previously, she headed the PR team at the Royal Botanic Gardens in Kew for three years.
This followed a nine-year stint at the Barbican's rival, the South Bank Centre, where she was also responsible for corporate communications.
She is unlikely to be directly replaced at Sadler's Wells. Instead, senior PRO Charlotte Hooper will oversee the six-strong press team when Hyde leaves. But it is not certain what Hooper's title will be.
Jones, who has been in her post since 2000, leaves the Barbican on 29 April to take up an Arts Council England-funded Executive Director Fellowship, based at Rambert Dance Company.