He escaped a driving ban, but had five penalty points put on his licence at Dumfries Justice of the Peace Court south of Glasgow.
Warne was represented by lawyer Graham Walker, who entered a plea of guilty on behalf of the leg-spinner, widely regarded as one of cricket's greatest players of all-time.
In remarks quoted by the BBC, Walker described the incident on the A74(M) motorway north of Gretna in September as an "error of judgement".
The prosecutor told the court Warne, driving on an Australian licence at the time of the offence, had been caught travelling at 103mph.
Walker added: "Warne is a man who had no previous convictions and no points on his driving licence and travels thousands of miles a year."
Apology for spatWarne also apologised for the foul-mouthed confrontation on Tuesday. He admitted he had gone too far in his on-field row but defended his right to show "emotion and passion".
"I'm very passionate when I play the game. I overstepped the line and hence I'm missing a game," Warne said.
On Monday he was banned for one match and fined Aus$4,500 (US$4,700) for the clash.