The appointment comes days after Motorola ended a battle with Carl Icahn, a major Motorola investor, and accepted two of his nominees onto its board.
Motorola's loss-making mobile phone division will be spun-off as a separate company next year.
Dorman, a telecoms industry veteran, has previously served as chief executive at AT&T, and has held senior positions with a host of other telecoms firms. He was already on the Motorola board before his appointment.
Zander stepped down as chief executive of Motorola at the end of last year and the firm is still searching for a replacement.