The trio, who were judges on the Australian show for 11 seasons, made their last appearance on Tuesday night's 2019 season finale.
"Despite months of negotiation, 10 has not been able to reach a commercial agreement that was satisfactory to Matt, Gary and George," Network Ten chief executive Paul Anderson said.
New judges will be introduced in next year's season, he said.
Nine newspapers report the trio had demanded a pay rise of more than 40% to stay.
The announcement came amid calls for Ten to sack Calombaris after his Made Establishment company was last week fined $200,000 for underpaying restaurant workers to the tune of almost $8 million.
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He was also dumped on Monday from a West Australian tourism campaign.
Mr Anderson denied the MasterChef announcement was linked to Calombaris' troubles, saying the network had been in negotiations with the trio for a number of months.
"The reality is that we couldn't meet the demands of the three judges," he told Ten News.
In a post on Instagram on Tuesday night, Mehigan thanked fans and the MasterChef team and paid tribute to the "journey" they and the contestants had travelled.
He denied their departure was motivated by finances.
"To explain: "It was time to move on, have more free time to explore our own creativity"," he said.
"It was never about the money and never will be about the money. We couldn't agree on the term of the new contract for 2020 and season 12. Something we felt very strongly about."
Working together will continue to be "the most important thing for us", Mehigan said.
Calombaris likewise took to Instagram, saying the trio were "close" to signing a new contract for season 12, "however the dates just didn't align".
Preston posted on Instagram that the chefs were "really keen to continue but we were unable to agree to all terms for the new contract.
