A 16-year-old boy has been charged with two counts of murder after the friends from university were found on Saturday.
Tutors from Sheffield remembered them as enthusiastic and positive students.
'Always happy' Sarasota police said there was no known link between the suspect and the victims, who were found shot dead early on Saturday local time in the Newtown area of northern Sarasota.
They were murdered in a deprived part of Sarasota and local officers said it was "very unusual" to find tourists in this area.
Sarasota police said the former University of Sheffield students were not carrying drugs but would not confirm whether they had any money or weapons.
Ed Ferrari, Research Fellow from the university's Department of Town and Regional Planning, said Mr Kouzaris was committed to his studies and his "his positive outlook and humour were infectious".
The tutor said: "He was just the sort of student any lecturer would hope to have in their class."
Mr Kouzaris spent several months travelling in South America before his death, visiting Ecuador, Argentina, Brazil, Colombia and Bolivia.
He was on a three-week holiday in Florida staying with Mr Cooper and his family.
Mr Cooper worked as a tennis coach for inspire2coach, a company based at the University of Warwick.
Dr Jon Burchell, Senior Lecturer from the University of Sheffield's Management School, said Mr Cooper was a hard-working student and "popular among his peers".
The tutor said: "He had a good sense of humour and a range of plans for what he wanted to do after graduation."
Friends and family said Mr Kouzaris, who was known as Jam, "lived every day to the fullest", in tributes on his Facebook page.
His cousin Lynn Hucker wrote: "To a beautiful cousin who I will never forget. Always happy and full of life."
The Foreign Office said next of kin had been informed, consular staff were providing assistance and Sarasota police had launched an investigation and made an arrest.