David MacDonald, 25, was driving north on the A9 in a tanker when it began to drift across to the opposite side of the road.
It smashed into a lorry being driven by Gordon Cooper, 57, who died in the crash.
MacDonald admitted causing death by driving dangerously on the Perth to Inverness road, between Dunkeld and Ballinluig, while unfit to drive due to lack of rest and while above the speed limit.
Lord Bracadale deferred sentence for the preparation of a background report, but said MacDonald should expect a prison sentence when he returned.
The court heard two teenage friends of MacDonald were accompanying him on the journey and one, Luke McLean, screamed at him moments before the collision two days before Christmas in 2010.
Advocate depute Stephen O'Rourke told the High Court in Edinburgh: "In the moments before the collision Luke McLean recalls that their lorry ... very slowly began to drift across on to the opposite side of the road.
"He shouted 'Sumo' twice, which is the accused's nickname, but the accused didn't react.
"He then screamed 'Sumo' very loudly but by this time Mr McLean realised they were across the carriageway and about to collide with the lorry being driven by Mr Cooper.
"At that third shout the accused did react, pulling the steering wheel around to the left which brought the driver's side of the accused's lorry directly into the point of impact."
The collision brought Mr Cooper's lorry to a halt on the verge with the cab of the vehicle significantly damaged.
MacDonald's vehicle continued on and jack-knifed and the cab hit a concrete block. The tanker trailer rolled on to its side detached from the cab.
Mr Cooper, of Montrose, Angus, was later found to have suffered a fractured skull and bleeding within the brain along with other injuries.
MacDonald, of Aviemore, Inverness-shire, was thrown from the cab of his vehicle resulting in the loss of his right leg below the knee and a fracture to the left leg.
Mr O'Rourke said both the passengers in MacDonald's tanker, Mr McLean and Anthony Mackin, who were both 19 at the time, suffered minor injuries.
Both vehicles were travelling at 56 mph, the maximum allowed by their speed limiters, while a 40mph limit applied to their vehicle class on the stretch of road.
The advocate depute told the court: "An investigation was carried out by Tayside Police and a number of irregularities were identified in the tachograph records for the accused's lorry.
"In essence, however, it appears that he had failed to take sufficient rest on the period leading up to the collision."
MacDonald picked up his lorry from an Elgin garage before driving to his employer's yard and heading south to deliver the tanker load of syrup to a distillery in Girvan, South Ayrshire, before the return journey north.
The advocate depute said the deceased left a widow, Rosemary Anne, and sons Daniel and Alexander and added that the family were left devastated.