Mr Harte has been with the law firm since joining as a trainee in 1994 and a member of its management board since 2005.
He will replace outgoing chief executive Duncan Murray from February 1.
Last month, Morton Fraser announced it was merging with Macdonalds to create a combined firm with fee income of more than £17 million.
Mr Harte said that the deal "will be an important step in the growth of the firm".
He added: "We have ambitious plans for strategic growth in the right locations and markets, and we remain committed to delivering both quality and value for our clients.
"I am very excited about the opportunities which lie ahead for us."