Transport Minister Meegan Fitzharris will on Monday release the final costings for the project, three weeks after light rail started taking its first passengers.

Ms Fitzharris said the result, which she had forecast ahead of the system's April 20 launch, had validated the ACT government's promise to "[deliver] an affordable and sustainable light rail network".

Government figures to be released on Monday show the total cost for the design and construction of the 12 kilometre city-to-Gungahlin line was $675 million.

The result is $32 million below the project's anticipated cost in the contract signed with Canberra Metro in 2016.

That figure was revised down from a previous estimate of $783 million.

The final bill still exceeds a 2010 cost estimate of $614 million for stage one of light rail. In 2014, the then chief minister Katy Gallagher suggested her cabinet would not support a cost substantially beyond that figure.

A four-month delay to the launch of light rail meant Canberra Metro missed out on millions of dollars in payments from the ACT government to operate the service.

Ms Fitzharris last month said the delay, along with saved availability payments, was not the reason the project had come in under budget. She reaffirmed that position on Monday.

She said the result was the product of two factors: the clear terms of the original contract and the nature of the government's arrangement with Canberra Metro.

"Canberra Metro bore substantial risks in the construction of this complex project," she said. "The sheer number of resources dedicated by Canberra Metro to the project demonstrated its commitment to delivering a world-class light rail system for Canberra."

The lower-than-expected final bill meant the cost benefit ratio for the project had been adjusted from 1.2 to 1.3, she said.

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"That means for every dollar invested, Canberrans get $1.30 back in benefits, including better transport, lower congestion, more jobs and the increasing value of homes and businesses along the route," she said.

Ms Fitzharris said a more detailed breakdown of costings would be included in a project delivery report to be released in the coming weeks.

The cost and potential benefits of light rail has for years been the source of intense debate in Canberra. The project's total cost, including construction, operations and financing, was estimated at $939 million when the deal with Canberra Metro was struck.

A 2016 report from then auditor-general Maxine Cooper found the nominal cost - not discounted to today's dollars - would be as much as $1.78 billion over the project's 20-year lifespan.

The audit report urged caution against claims the project would deliver $198 million in wider economic benefits.

Ms Fitzharris this week said the light rail was already proving popular with Canberrans, with patronage tracking at levels not expected until 2021. The business case predicted 15,120 people would be riding the light rail in 2021.

Extra light rail services had been added during peak periods to cope with demand, Ms Fitzharris said.

The government has offered free trips on light rail and its buses between April 29 and May 26 to allow Canberrans to familiarise themselves with the revamped public transport network.

"Along the light rail corridor the benefits are plain to see: with light rail getting people to work, opening up new customers to local businesses and seeing hundreds of Canberrans employed on building and construction projects along the alignment that are already using their proximity to light rail to attract buyers," she said.