A minority group of independent councillors ran the local authority before the local council elections earlier this month.
The new coalition was formally set up at the first full meeting of the new council in Inverness.
Independent Margaret Davidson was re-elected as leader and Lib Dem Alasdair Christie as depute leader.
Independent Bill Lobban was elected convener.
SNP councillors challenged the appointments while the Conservatives challenged the appointment of Ms Davidson, but both challenges were defeated.
SNP councillor Maxine Smith has been confirmed as leader of the main opposition group.
The results of the elections saw 28 independent candidates elected, followed by the SNP on 22, Conservatives and Liberal Democrats with 10 each, Labour three and Scottish Greens one.
The Conservatives were the first to be elected to Highland Council in 22 years.
Pippa Hadley's win for the Scottish Greens was a first for the local authority, which had no representative from that party previously.

The Slovenia-born 26-year-old beat 30-year-old Czech Rosol 6-2 6-3 in just over an hour.
Spaniard Nadal, 29, is the fifth seed and received a bye into round two.
British number one Andy Murray also enters at the second round and will play French qualifier Pierre-Hugues Herbert, 25, on Tuesday.
The 28-year-old Scot is also competing in the men's doubles, where he and partner Dom Inglot progressed to the second round by beating Pablo Cuevas and Marcel Granollers 6-3 6-4.
Murray and Englishman Inglot next play Edouard Roger-Vasselin of France and Serbia's Nenad Zimonjic.

The announcement was made on the official Star Wars Twitter page.
Fans will have to wait for more details to be released as the makers of the films are keeping things top secret so nothing gets given away.
It is believed the film will focus on what's been going on with Luke Skywalker, one of the biggest characters in the series.
The Last Jedi will take place directly after the events of 'Star Wars: The Force Awakens', which ended with Rey (Daisy Ridley) finding Luke. Will Luke be the last Jedi in the title?
But, fans will have to wait until December to find out exactly what this film has in store for Rey, Luke Skywalker and the rest of the rebels.
Star Wars: The Last Jedi will be released on 15 December 2017.

Edward James, 75, was convicted of fraudulent trading at Crown Currency Exchange, where he was a director.
He used new customer cash to pay off old clients for two years, Southwark Crown Court was told.
More than 12,000 people were left £20m out of pocket after the Cornwall-based firm collapsed in October 2010.
Three other people involved in the scam were jailed in June.
Crown Currency director Peter Benstead, 72, killed himself during the trial.
Benstead spent customer cash on a £900,000 luxury house in Penzance, a second home in the Dordogne and spent £36,000 on a seven week cruise.
Jurors were told James, who stood down as Tory chairman of Mendip District Council in the wake of the allegations, knew the dire state of the company.
Judge Michael Gledhill said James' public service to Glastonbury as mayor in 2009, "paled into insignificance" in comparison to his role in the frauds.
A Highland Council administration made up of independent, Liberal Democrat and Labour councillors has been agreed.
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British number two Aljaz Bedene will play Rafael Nadal at the Monte Carlo Masters after beating Lukas Rosol in round one.
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'Star Wars: The Last Jedi' will be the title of the latest instalment of the popular sci-fi series.
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A former mayor of Glastonbury has been jailed for 42 months for his involvement in a foreign currency exchange scam.