The vaccine was only delivered to Scotland at the start of the week with NHS Greater Glasgow and Clyde (NHSGGC) becoming the first health board north of the border to roll out the first doses.
People who visited the vaccination centre at the SSE Hydro in Glasgow on Wednesday were given Moderna including Alistair McMaster.
The 55-year-old, whose mother received AstraZeneca, told the PA news agency: “It was fine, easy, no pain or anything.
“I asked what one it was and (the nurse) said it was the new one just tried out today for the first time – so a wee bit of a surprise, but worth a try.”
Sam Ferguson and Heather McGregor were also both surprised to find out they were also among the first.
Mr Ferguson, 52, said he had been talking to workmates who “were not sure” about AstraZeneca, admitting recent news “puts a doubt in your mind”.
As the new vaccine was given to people across the UK, it emerged those aged 18 to 29 will be offered Moderna, Pfizer or other jabs instead of AstraZeneca over a possible link with “extremely rare” blood clots.
Ms McGregor, 53, added: “Like everybody else, you want the safest one out there.
“The Moderna one from what I’ve heard is probably the better one out of the two. Better being safe than sorry.”
Natasha Quinn, 19, was happy to be one of those receiving the Moderna jab on Wednesday.
She told PA it was “like a normal jag you’d get for the flu” and that while she “wasn’t really worried for coming” to the Hydro, she was worried about receiving AstraZeneca.
The concert venue formed part of the NHS Louisa Jordan hospital, which closed at the end of March having opened in the Scottish Event Campus (SEC) last year.
The UK has bought 17 million doses of the Moderna vaccine, with Scotland set to receive an amount proportional to population – a little under 1.5 million.
Addressing the coronavirus briefing in Edinburgh on Tuesday, First Minister Nicola Sturgeon said: “The fact that we now have three vaccines in use is clearly very welcome and it does give us greater security of supply which is welcome.”