The competition was thrown open to a public vote and attracted more than 40, 000 votes on Twitter.
The two hilarious winning names were 'Gritsy Bitsy Teeny Weeny Yellow Anti-Slip Machinery' and 'David Plowie'.
Celebrities including American singer Curtis Stigers, comedian Bob Mortimer and paralympian Tanni-Grey Thompson took to Twitter to praise the competition.
Stigers, who had a top 10 hit in the early 1990s with 'I Wonder Why', suggested 'Grit Balls o’ Fire' for one of the truck’s names and said the naming campaign had even been mentioned on a radio station in Idaho in the US.
Doncaster Council tweeted to praise him for his entry and said: "You’re very good at this for someone who has never entered a gritter naming contest before."
Former Shooting Stars host Bob then messaged him to say: "Curtis Stigers has today been tweeting Doncaster Council about their gritting machines, surely that's all you need to know."
Stigers replied: "Thank you Bob for singling out my important work in the gritter tweet industry."
Tanni-Grey Thompson said the competition "made her smile."
Gritsy Bitsy, a play on the words of Brian Hyland's 1960 track Itsy Bisty Teenie Weenie Yellow Polkadot Bikini, was put forward by Natalie Washington, aged 34.
She said: "When you go on courses or whatever, and you have to say an interesting fact about yourself, well I've got one now.
"I can say I've named a gritter."
The two finals saw David Plowie beat Basil Salty with 58 per cent of the vote, while Gritsy Bitsy won a tighter contest with 53 per cent of the vote against Spready Mercury.
Hundreds of names were sent in to the council before a panel reduced that to 16 potential names which would face the public vote.
The final pairings were decided after the most successful four names were drawn from a pot.
A council spokesman said: "It seems to have cheered Britain up. It's been amazing and got people interested in gritting."
Other gritters in the council's fleet include Brad Grit, Gritney Spears, The Subzero Hero, Mr Plow, and Usain Salt.