Tenders for the construction closed at the end of October.
On Wednesday, one of the project’s most vocal critics, said he was "chuffed" to be proved wrong.
The 1883 Thames St courthouse has stood vacant since it was identified as requiring earthquake strengthening and was closed in November 2011. When the budget for the required work went to the council, only Cr Guy Percival voted against the plan.
"I was quite vociferous about it, too," Cr Percival said.
"I am absolutely over the moon. I think [council property manager Renee Julius] has done a great job.
"At the time, I said I 100% support the project, but I had no faith they could do it for that money. I have been proven wrong and I am absolutely chuffed."
The original government estimate to strengthen the courthouse was up to $6 million, but the council took ownership of the building last year and negotiated a lease with the Ministry of Justice. The ministry was expected to remodel the building at its own cost, before court services resumed.
Mrs Julius said both tenders came in under $900,000, which was "fantastic", both indicated work could begin in late January or early February, and both expected the work to be completed within 26 weeks.
The contractor would use covered scaffolding and the work could be undertaken whatever the weather. Deputy Mayor Melanie Tavendale said even though the council had earlier predicted a start on the work by this month, the fact the tenders came in "within the cost envelope" was "a fantastic step forward".
"Whether you start something in November, or January-February, is literally the Christmas break. And that’s the way it all falls. We’re quite comfortable with the timeframes. We think that getting any movement forward is a win for our community."
Oamaru court services have mainly been held in a portable facility, known as the "porta-court", in Humber St, since the closure of the courthouse.
