The former Falkirk, Hibernian and Livingston boss has signed a two-and-a-half-year deal with a team who are sitting in second place in the Scottish Premiership and still in both cup competitions.
Hughes has been without a job since his contract was terminated at Hartlepool following a six-month spell in which he was unable to keep them in League One.
The 49-year-old described his appointment as an "honour and a privilege".
He added: "It's very important that I immerse myself in the character and fabric of the football club and community.
"If I step aside from the football and speak about the people of Inverness, I get the feeling they want a real honest day's shift, they want to roll their sleeves up and are honest people.
"I feel that's the values this football club is built on so that makes it a right good fit for me."
Inverness secured their best finish last season - fourth - and began this campaign in even better form under Terry Butcher and assistant Maurice Malpas, who left for Hibs last month.
The team are on a five-match winning streak ahead of their trip to St Mirren Park on Saturday and Hughes plans to keep their approach on a very similar tract in order to maintain the standards.
"It's going to be very difficult but if we can keep playing on this underdog tag that the club loves to play on, hopefully we get that success," he said.
"I just feel the club needs a manager with a personality and experience. I just feel I am the right fit.
"It's going to be difficult, Terry has done a wonderful job, but it's a challenge I am really excited about. It's carry on regardless."
The former Celtic, Hibs and Falkirk defender secured the position ahead of the likes of Alloa boss Paul Hartley and former Kilmarnock manager Kenny Shiels and Inverness chairman Kenny Cameron stated he was the only candidate offered the job.
Cameron said: "John's appointment was the unanimous choice of the board.
"He is an experienced manager which is what we feel is required in the current scenario we have at our club. He greatly impressed all the directors with his knowledge of the club, his passion and philosophy for the game.
"We took our time about the appointment as it was important to obtain the right fit for this stage of the club's development. John was the person who met our criteria."