Salisbury and Ram went into the final on Rod Laver Arena as the favourites against Australian wild cards Max Purcell and Luke Saville and justified that with a 6-4 6-2 victory.
Salisbury follows in the footsteps of Jamie Murray, who won this title in 2016 with Brazil's Bruno Soares, and joins the Scot, 2012 Wimbledon champion Jonny Marray and Roger Taylor as the only British winners of slam trophies in men's doubles in the Open era.
British interest in doubles still centres on Murray but 27-year-old Londoner Salisbury has enjoyed a rapid rise to become the country's leading exponent in the format following a surprise run to the Wimbledon semi-finals in 2018.
Salisbury and Ram qualified for the ATP Finals together for the first time in November and this title will lift them to four and five in the world rankings, respectively.
They are not planning to stop there, with Salisbury saying: "We set some goals at the end of last year. One of them for this year as a team was to win a grand slam, the other one was to finish the year as the number one pair."
Glandular fever affected Salisbury badly as a teenager but he still had hopes of making it as a singles player after going to college in the United States.
It was not until 2017 that he made the switch to doubles full-time, with his Wimbledon run the following year alongside Dane Frederik Nielsen proving a watershed moment.
"Before that, I was thinking I could be a good doubles player," he said. "I wasn't really sure how high I could get. Once I did that at Wimbledon, then I kind of realised the level that I could play. It was possible to win a grand slam.
"I guess it shows, even if you're not one of the top juniors, winning all the junior grand slams or breaking through when you're 19, 20, that you can still have a very good career.
"Obviously, it's still early days for me. I think it should give a lot of belief to other players that, if you keep working at it and you have the right support, you can do it."
With their matching long, blond hair, Purcell and Saville looked like they would be more at home surfing at nearby St Kilda beach.
They were not to be underestimated, though, having taken several impressive scalps this fortnight as well as a string of title wins on the second-tier Challenger Tour.
They were under pressure from the start and Ram and Salisbury might have forged ahead before they broke the Saville serve at 3-3 in the first set.
They did not face a break point throughout the match and Salisbury in particular was outstanding.
Ram won the mixed doubles here 12 months ago but, at 35, this was his first men's doubles title in his 58th slam tournament, setting an Open era record.
The American was full of praise for Salisbury, saying: "He doesn't show it outwardly, but he's incredibly competitive, especially on the tennis court.
"I think just his ability to rise to the occasion is pretty special. Obviously he's an incredible athlete, too.
"But I think one thing that's helped us is we've become really good partners. When we're nervous in tough situations, we're not afraid to say what we think."
The trophy came with combined prize money of 760,000 Australian dollars (approximately £385,000), and Salisbury revealed another of his goals for the year is to move out of his sister's flat in Peckham and buy a property.
He said: "We tried to stay in the moment, not think about what would happen if we win. I think that's the next thing on the list, looking to buy a place sometime this year."