The NZ Transport Agency has encouraged the public to plan their journeys and expects it will take some weeks for traffic flows to adjust.
NZTA Auckland highway manager Brett Gliddon said it was still early to say exactly how much time people could save, but said it would benefit many people, from those travelling south to north, to people going to the airport and those travelling from the west.
It should also cut rat running and traffic on local streets.
Motorists were patient today, following signs, sticking to the speed limit and not changing lanes inside the tunnel.
All systems in the 2.4km long twin tunnels had worked as they were designed, Gliddon said.
But Monday will be the real test.
"It's going to be really busy and many people will be using the new route for the first time so we're asking everyone to be patient and factor in extra travel time for the next few weeks while things settle down.
"We will continue to keep a close eye on traffic flows and adjust traffic control signals and other tools to help keep traffic moving across the wider road system."
Gliddon urged people to leave the sightseeing for a few weeks, pointing out the tunnel "will be here for a while".
The NZTA said the tunnel is not designed to remove peak time congestion but provide "a better balance of traffic flows across the road network, including helping to remove cars from local roads".