Charlotte Wright, the agency's director of business and sector development, has been in the role in an acting capacity since last August.
HIE's previous chief executive, Alex Paterson, left to join Historic Environment Scotland.
Headquartered in Inverness, HIE works with businesses and communities in Argyll, Highlands, Moray, Western Isles and the Northern Isles.
It has a budget of Â£65.9m for 2017-18, including Â£55.7m from the Scottish government, to invest in developing businesses, economic sectors and communities.
The agency also co-manages the Scottish Land Fund with Big Lottery Scotland, operates Community Broadband Scotland and has subsidiary renewable energy company, Wave Energy Scotland.
Rural Economy Secretary Fergus Ewing said: "Charlotte has proven herself as an exceptional leader who is absolutely committed to making a difference in every part of the region, and I am certain she will be a highly effective and inspiring chief executive for years to come."
In March this year, plans to replace the boards of Scotland's enterprise and training agencies with one national board were abandoned.
Economy Secretary Keith Brown said HIE, Scottish Enterprise and Skills Development Scotland would continue with their own boards.
He also announced that a national strategic board would be set up, to "align the work" of the agencies.
Opposition parties welcomed the news but said the minister had been forced to make a u-turn.
Highlands and Islands Enterprise (HIE) has appointed a new chief executive.