The 36-year-old succeeds Spanish maestro Juanjo Meno, who has led the orchestra for seven years.
Mr Wellber has been Music Director of the Raanana Symphonette Orchestra in Israel since 2009 and last month became Principal Guest Conductor at Semperoper Dresden.
In January 2020 he will become music director of the Teatro Massimo di Palermo.
Simon Webb, the BBC Philharmonic’s general manager, said: “Having seen Omer conducting a number of orchestras over the last year I have been fortunate to have experienced his brilliance first hand in a wide range of repertoire.
“His immediate connection with the BBC Philharmonic was evident in his first concert and we are now delighted to have secured one of the most sought after young conductors of his generation.”
