She will succeed Clive Gillinson, who will take up the post of executive director and artistic director of Carnegie Hall this summer.
McDowell is currently director of the City of London Festival, and has previously held executive posts at the Wales Millennium Centre, Arts Council England, Scottish Chamber Orchestra, and the Ulster Orchestra.
In a statement, McDowell said, "I am much looking forward to taking up post with the LSO after the 2005 City of London Festival. The challenge of the LSO's second century offers great opportunity to build on the orchestra's excellence on the concert platform at home and abroad."
The orchestra is celebrating its centenary this season.