The altar, discovered by Beckfoot volunteer John Murray, has lain buried for uo to 1,600 years.
Tony Wilmott, site director of the Maryport excavation, said that it was the most exciting find he had known in 42 years as an archaeologist and 25 years working on Hadrian's Wall.
He said: "I bought a bottle of whisky at the Birdoswald dig 25 years ago and offered it to the first person to find something like this.
"This time, the whisky went to John Murray."
The excitement started soon after 9am on Wednesday when Mr Murray, 68, who was also responsible for finding a hoard of Roman coins a couple of years ago, was working in a pit previously excavated in Victorian times.
He said: "There was a lot of rock around and I noticed a piece with a line on it. I thought it might be a piece of something."
He called Mr Wilmott and the two men carefully uncovered it.
Mr Wilmott said: "By lunchtime I was so sure of what it was that I went to the Maryport Co-op and bought John his whisky and some bubbly to share with the volunteers when the job was done."
The men worked until after 6pm on Wednesday to get the altar out and then carry it carefully to the nearby Senhouse Roman Museum, where it was kept on Wednesday night.
By 8.30am yesterday there was a line of volunteers queuing at the door to check the find.
Mr Murray said he only became interested in archaeology after he retired six years ago and had never imagined he would find anything as historically important as the altar.
It was lying face down and was surrounded by building stones.
The altar discovered this week was to the god Jupiter and was inscribed on behalf of Attius Tutor from the First Cohort of Baetasian, from the lowlands of Holland. This Roman cohort moved from here to Kent and appeared to be specialists in coastal defence.
The altar is the fourth by Attius Tutor to be found, and three others form part of the Senhouse collection, unearthed in 1870.
There are two other collections of four altars by the same people at the museum – one for Marcus Maenius Agrippa and one for Gaius Caballius Priscus.