The coffee shop has been built by Trebor Developments and ASK Developments next to the Porsche dealership on the site.
It leaves just over half an acre at the prominent site, at the top of the A449 Stafford Road in the city, remaining to be developed. The companies say it is "suitable for a range of roadside uses".
Tom Swords from Whitbread, owner of the Costa Coffee chain, said: “We are really looking forward to opening a new drive thru store in Wolverhampton , bringing 18-20 new jobs to the area.
"As the nation’s favourite coffee shop brand we are looking forward to being an active part of the local community, getting involved with events; providing the store as a meeting place and helping with fundraising.”
Costa is on a growth spree in Wolverhampton. It already has two city centre outlets and has just sought permission from Wolverhampton planners to convert the former Wolves Shop in Dudley Street into a coffee shop.
Bob Tattrie, managing partner of Birmingham-based Trebor, added: “It is always good to see a new development completed on site and this Costa drive thru complements the high quality of the Gateway site, sitting next to the Porsche dealership. We do not expect the final plot to be available for long, given the prominence of the site and the adjoining uses."