Mr Morgan, who walked up to the summit this morning for the ceremony, called Snowdon "one of the wonders of Wales" and said the new visitors centre "does justice to that proud and very ancient mountain".
He added: "This new centre will allow visitors of all ages and physical ability to learn more about the mountain's significance as a unique recreational, environmental and cultural resource."
Snowdonia National Park Authority chairman Caerwyn Roberts said it was one of the most important days in the history of the national park.
The building was designed by architect Ray Hole, and is built to withstand extreme weather conditions.
Winds can reach 150mph, the annual rainfall is more than 5m and the temperature can get down to minus 20 degrees centigrade.
Poor weather meant more than 70 construction days were lost.
More than half a million people walked or took the train up Snowdon last year.
Tegwyn Williams was the man in charge of the site for contractors Carillion, and he admits that he is glad the project is coming to an end.
More than once I've thought we'd never get here
Tegwyn Williams, clerk of works
"More than once I've thought we'd never get here," he said.
"We've had days when we could not get here.
"We've had to walk down to Rocky Valley (half way) at the end of a working day because the train could not get to us... and it was scary when the whole train rocked because of the wind.
"But it's good to see it finished and it looks good," he added.
Snowdonia National Park Authority chairman Caerwyn Roberts said it was one of the most important days in the history of the national park.
Mr Roberts said the official opening of the granite structure was a "celebration" of the success of the initiative to replace the old Snowdon cafe, which was built in 1935 and designed by architect Sir Clough Williams-Ellis.
"Five years ago the authority decided to commit the equivalent of its entire annual budget to one project, a project located 3,500ft up at the top of a mountain," said Mr Roberts.
"If it wasn't for the determination and the perseverance of staff, members, and especially the builders, we wouldn't be here today and therefore I sincerely thank them," he said.
The cafe part will open from 0800 BST to 2000 BST each day, and the staff who remain on-site will ensure that it will open even if the train cannot bring in the day staff.
There is also a shop area, toilets, disabled lift, and the whole area in the building is used as an interpretation space.
The cafe opened to the public from 1400 BST on Friday.
Advertisement
First Minister Rhodri Morgan walked to Snowdon's summit before paying tribute to those behind the new visitors centre
Bookmark with:
What are these?