Work is still underway on the project and workers have been seen working outside the station this week - but a completion date has yet to be given.
The extension will run from a junction with the existing Metro system, close to the current terminus at St George’s, through to the railway station.
Wolverhampton Council's leader Ian Brookfield said he was looking forward to it opening and voiced some disappointment at how long the work had taken.
"It is an absolute priority that it is open for the Commonwealth Games," he said.
"There will be big benefits. It is going to be one of the best interchanges in the country.
"It will be a fantastic gateway to the city and will keep people coming in."
Councillor Wendy Thompson, opposition leader on the council, said she would be glad when the work had finished.
She added: "I think it's taken an extraordinary long time. It's caused a lot of disruption to businesses and drivers have been unsure which way to go.
"When work needs to be done it needs to be done as efficiently and quickly as possible.
"I understand there has been Covid and some issues but we are not talking about a short amount of time."
Midland Metro Alliance, which is working on behalf of the West Midlands Combined Authority and Transport for West Midlands to construct the extension, hopes it will encourage more people to use public transport and benefit the local economy.
The first phase of constructing this route was completed in 2017.
Last year, a total of 40 metres of double track was installed on Railway Drive and September also saw the installation of the extension’s switch and crossing, an intricate section of rail that allows trams to move from one track to another.
The Wolverhampton city centre extension includes three new Metro stops.
Two of these – one on either side of the road – will be in Pipers Row to allow easy interchange to and from the city’s bus station and one will be at Wolverhampton Railway Station, where the Metro will terminate.
A Midland Metro Alliance spokesman said: "The Wolverhampton City Centre Metro extension is currently in the final stages of construction following the start of works outside the revamped Station Plaza last year.
"Track has now been installed in this area and further activity, such as delivering system integration works including upgrading and commissioning a substation and final building activities such as fixing overhead lines to key buildings, are currently taking place.
"Much of this activity is taking place outside of regular working hours. We are working closely with all partners to accelerate activity in order for testing and commissioning and driver familiarisation to commence before the route can open.
"We hope to be able to advise passengers of an opening date soon.”