Northern New Zealand will see cloudier, windier and milder weather as it hits, but the South Island will be the worst affected.
"We're looking at possible northwest gales on Thursday and into Friday in Southland, up into Otago, Canterbury and Wairarapa," Coutts said.
Heavy rain is also on the cards for the west of the South Island this weekend, Coutts said.
"For the most part the South Island will be smack bang under the centre of this weekend high – so the cold southerly change at the end of this week will be locked in, seeing overnight lows plummet to possibly -5C through well inland areas like Tekapo, Weatherwatch says.
"Queenstown, Alexandra and Cromwell have overnight lows currently forecast between -1 and -3C this weekend, but some locations within, or near, these areas may dip to -5C, creating heavy frosts."
Cromwell, Clyde and Alexandra will awaken to a chill -4C on Saturday morning, but the coastal main centres of the South Island won't see temperatures as low.
Coutts said exposed areas of central Otago and south Canterbury will be the coldest, with a "pretty frosty weekend" expected in inland areas.
But the brunt of the weather should be over by Sunday, he said.
Niwa meteorologist Ben Noll earlier said the approaching high also came nearly a year after a similarly dramatic system drifted over the country, which pushed air pressure to 1043.2 hectopascals (hPa).
"For the upcoming weekend, it looks to possibly centre over the top of the South Island where the highest pressures will likely be."
Atmospheric pressure is the force of air pulled towards the earth by gravity. The highest pressure recorded in New Zealand was in Wellington in 1889 at 1046 hPa.
Noll said the highest values ever recorded for this month was the 1044.7 hPa measured over the South Island on June 5, 2016.
"The modelling we have for the feature coming this weekend shows it could be in the low 1040s, which puts us in the ballpark of where we could be talking about near record, or even record values, for surface pressure in the atmosphere."
He warned that people would need to watch out for black ice and frosty driving conditions as the worst of the weather hits.
"We are talking about temperatures as cold as -15C in some low-lying areas about the alps on Saturday morning, creating some pretty frosty conditions," he said.
"These are some pretty extreme cold anomalies, so no doubt people will have to watch out for things like black ice."