Sharpe takes up the role after the departure last week of Tom Swarbrick, who will return to LBC as a presenter, having left the radio station to take up the role in August 2016.
Sharpe had been working in Number 10 since the start of the year, working on domestic political press relations.
He spent the second half of 2017 as a special adviser to First Secretary of State Damian Green, before Green was sacked after it was found to have made "inaccurate and misleading" statements around claims pornography had been found on his work computer in 2008.
Green, a close ally of the Prime Minister, was also under pressure over alleged inappropriate behaviour towards Kate Maltby.
Before working for Green, Sharpe spent three years as head of PR for The Sun, also writing leaders for the paper towards the end of his tenure, during which time he handled the news that the paper was withdrawing topless women from its infamous Page 3.
Earlier in his career he worked for the agencies Pagefield and iNHouse Communications, among others.
Sharpe was a judge at the PRWeek UK Awards 2017 and has contributed several articles to the magazine.