Sydney's new status as a two-airport city is already causing confusion for some travellers.  

Julie Lundmark, from Sweden, headed to Melbourne for the weekend from Sydney Airport but was surprised to discover her return flight landed at the brand new Western Sydney International Airport (WSI).

The airport, which has been decades in the making, began operating passenger flights on Sunday.

Ms Lundmark and her friend were on Jetstar flight JQ373 when they realised the mistake.

"We landed here and looked out of the window and had no idea where we were," she said.

"And we looked down the map and we thought to ourselves, we are a little bit lost."

She said she had checked the name of the airport on her boarding pass a few days ago.

"The funny thing is we googled because we didn't recognise the name 'west airport' that was on the boarding pass, and we googled it and it took us to the normal Sydney airport."

Ms Lundmark said they were left looking for ways to get back to Sydney Airport.

"We have our car parked at the other airport," she told 702 ABC Sydney.

"We are stuck in Western Sydney."

A metro service from St Marys to WSI was not completed before the airport opened, with buses and a free shuttle operating to and from the station being the main public transport options until the rail link opens.

However, Ms Lundmark said given it would take her two hours to get to Sydney Airport, she hoped a friend with a car would help out.

"We've made some panic calls to the city and hopefully someone will pick us up," she said.

"Double check, everyone, on your tickets before."

'I'm meant to be in Perth'

Ms Lundmark was not the only confused traveller at WSI this morning.

One man who disembarked flight NZ165 from Auckland said he thought he was travelling to Western Australia.

"I got confused, I saw Western Sydney," he said.

"I thought it was Western Australia, and I'm meant to be in Perth, but look, it's still pretty fun, so we'll make the best of it.

"I realised by the time I got on the flight that that's not where it was going, but we'll figure it out. 

"I'm on holiday, so it's not the worst thing."

Some of the first passengers to travel through WSI have praised the new $5.6 billion airport terminal's layout and operation.

Three domestic Jetstar flights are scheduled for today, with Air New Zealand flights this morning marking the first international departure and arrivals.

Seven carriers have signed up to operate out of WSI.

Flights to Singapore are scheduled to start soon, with other destinations including Nadi in Fiji, Ho Chi Minh City and Doha to follow.