L/Cpl Gillon, 26, was described as a “larger than life soldier” who was “destined for great things”.
Earlier, Foreign Secretary Dominic Raab condemned the attack – that also killed two Americans – as “cowardly”.
He said those responsible would be held to account and that it was “essential to defend against these deplorable acts”.
At least 12 people were injured in the attack on the Taji military camp, north of Baghdad, on Thursday.
It came amid heightened tensions between the US and Iran.
The Iraqi military has opened an investigation into the attack.
The Ministry of Defence said L/Cpl Gillon – a member of the Royal Army Medical Corps and a reserve with the Scottish and North Irish Yeomanry – was a “fit, energetic and compassionate individual”.
She also had a career as a self-employed sports physiotherapist. It was understood she was from South Ayrshire.
Her commanding officer, Lt Col William Leek, described her as a “hugely popular character”.
“She was a larger than life soldier who was determined to deploy on operations, help others, develop herself and gain practical experience.
“She had already achieved a great deal in her relatively short time with us and it was abundantly clear that she was destined for great things in her civilian and military careers. Her loss is keenly felt.”
Her squadron leader, Maj Craig…