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The 52-year-old replaces Richie Foran, who was sacked following relegation from the Premiership.
He has signed a two-year deal after leaving his head of coach education post at Hearts, where he spent 18 years at a player and manager.
The Highlanders won promotion to the top flight for the first time under Robertson's guidance in 2003.
Robertson left in 2004 to take over at Hearts and has had spells in charge at Ross County, Livingston and Derry City.
He has not held a managerial position since leaving East Fife in March 2012.
"This time last week it wasn't even on the radar," Robertson said of the job. "I didn't apply for the job, I had a very responsible, high-profile job at Hearts - commercial and the academy, working as head of coaching there to rebuild it.
"I was as surprised as anybody when the call came in to say, would you like to come up and have a chat?
"This is a massive challenge and one I'm looking forward to, and it's one we can achieve together as a club. We know what's ahead of us. It's far easier to stay in the Premiership, I think, than get out the Championship, but it's a challenge we're going to meet head-on.
"The fans' expectations will be high, and they should be, but they'll not be any higher than mine."
Caley Thistle chairman Willie Finlayson added: "We had an excellent interview process with some strong candidates but John emerged as our unanimous choice.
"We were hugely impressed with his tremendous drive, determination, communication and motivational skills.
"He clearly has a great knowledge of the game in Scotland and is both well respected and connected. We firmly believe he is the right man to lead us back into the Premiership."
After the departure of John Hughes, Foran was promoted to player-manager last summer on a four-year contract, having been at the club since 2009.
They won three of their last five fixtures but could not avoid finishing last and dropping down to the Championship.
Chairman and chief executive Kenny Cameron stood down three days after relegation was confirmed.
Aberdeen granted Inverness CT permission to speak to Under-20s coach Paul Sheerin about their managerial vacancy before deciding Robertson was the man to take them forward.

British Heart Foundation Cymru (BHF) wants emergency life support (ELS) skills on the national curriculum, including cardiopulmonary resuscitation (CPR).
BHF says such a move would create a new generation of lifesavers across Wales.
The Welsh petition has collected 4,000 names since being launched in February.
The charity wants to teach children first aid skills, such as resusciation techniques, incorporating them into areas of the existing curriculum.
"If they are properly trained they are as capable as adults and by acting promptly they can prevent disabilities and help save lives," Delyth Lloyd, public affairs manager for BHF Cymru, told BBC Radio Wales.
She said ELS are a set of actions which can "keep someone alive until professional help arrives" such as CPR which can include rescue breaths and chest compressions.
Ms Lloyd acknowledged that while it is not currently a compulsory part of the curriculum some schools do teach ELS skills.
"We'd like to see a new generation of lifesavers across Wales with every child leaving secondary school knowing how to save a life," she said.
Across the UK over 100,000 people have signed the petition.
John Robertson is the new manager of Inverness Caley Thistle, returning to the club he left almost 13 years ago.
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A petition has been handed over to the Welsh assembly calling for first aid to be taught to all pupils in secondary schools.