LONDON—The BBC announced Thursday that it has appointed Deborah Turness as its new chief executive for news and current affairs, bringing to the broadcaster a vastly experienced journalist who previously held senior leadership positions at the news division of American TV network NBC. Turness, 54, comes to the BBC from British media company ITN, where she is currently CEO. The native of England will replace Fran Unsworth, who is leaving at the end of January. “In the U.K. and around the world there has never been a greater need for the BBC’s powerful brand of impartial, trusted journalism,” Turness said in a statement. “It is a great privilege to be asked to lead and grow BBC News at a time of accelerated digital growth and innovation, when its content is reaching more global consumers on more platforms than ever before,” she added. BBC Director-General Tim Davie said Turness “brings a …