Rourke was born in 1976 in Salford, Greater Manchester, to Vivienne and Sean Rourke. She has one brother, Damian. She attended St Mary’s RC Primary School, Swinton, St Gilbert’s RC Primary School, Winton, St Patrick’s RC Secondary School, Eccles, and Eccles College of Further Education.

Upon graduating from Cambridge in 1998, she worked for Cambridge Arts Theatre, co-ordinating the BT National Connections project around East Anglia. She then moved to London, where she worked nights as a secretary for a mergers and acquisitions bank, pursuing theatre projects during the days, including assisting Laurie Sansom on a production of J.B. Priestley’s Dangerous Corner at Watford Palace Theatre. After nine months of living and working in London, she was appointed Resident Assistant Director at the Donmar Warehouse. Sam Mendes was then the Artistic Director. Over her year-long traineeship, she assisted Michael Grandage on Peter Nichols’ Passion Play and Merrily We Roll Along, Nicholas Hytner on Orpheus Descending starring Helen Mirren, Sam Mendes on Nick Whitby’s To The Green Fields Beyond and Phyllida Lloyd on David Mamet’s Boston Marriage, starring Zoe Wanamaker.

In 2008, Rourke was appointed Artistic Director of The Bush Theatre, one of the country’s key venues for new plays and playwrights. During her time at The Bush, she programmed the first plays and early work of, amongst other writers: James Graham, Nancy Harris, Lucy Kirkwood, Nick Payne, Penelope Skinner, Jack Thorne, Steve Waters, Anthony Weigh and Tom Wells. Shortly after she was appointed, The Bush Theatre was the target of a proposed cut in funding by Arts Council England. Josie made a Freedom of Information Act request which established that the proposed cut had been made using flawed evidence and data. The Arts Council reinstated the theatre’s funding but gave Josie three years in which to find a new home for The Bush Theatre. In 2011, The Bush Theatre opened in new premises in a former library building, winning Theatre of the Year. The new home for The Bush opened with Sixty-Six Books, a twenty-four hour performance cycle with 66 writers and 144 actors that Josie co-directed with a dozen of her peers. The cycle went on to be performed overnight in Westminster Abbey.

In 2011, Rourke was appointed Artistic Director of the Donmar Warehouse, the first woman to hold the role and the first female theatre director to be appointed the artistic director of a major London theatre.

Since 2012, Rourke has been a Non-Executive Director of public service broadcaster Channel 4.

In 2019 Rourke became a Vice-President of The London Library.