James Stark, 37, Steven Sheldon, 35, and Martin Williams, 36, all from south Wales, died in Wiltshire in June 2014.
Stephen Jenkins, 39, of Abercwmboi, was driving a van that crashed into a lorry, near Chippenham.
He was convicted of causing death by dangerous driving at a previous hearing at Swindon Crown Court.
Speaking after sentencing, Sgt Barrie Card, from Wiltshire Police, said: "Falling asleep at the wheel doesn't happen straight away, you will get telltale signs and that's when you must act before it's too late.
"Every driver owes it to themselves, their passengers and other road users to make sure they are fit to get behind the wheel, and that includes not being too tired.
"The road safety message 'tiredness kills' is true and sadly so true in this tragic case."
Jenkins, of Park View Terrace, was also disqualified from driving for four years and three months and will have to take an extended retest to get his driving licence back.
A van driver who killed three passengers in a crash on the M4 after falling asleep at the wheel has been jailed for four-and-a-half years.