The Italian had ordered all the players and coaching staff to return from their summer breaks by letter last month and spoke to each of them individually on Monday.
The players, some of whom had to cancel or cut short their summer holidays, have been told to report back for pre-season training on June 26.
Leeds are 20/1 to win the Championship title next season and the 57-year-old told the club's official website: "I met all the players on Monday and they showed me that they wanted to stay at the club.
"They work for the club, not Massimo Cellino. They showed me respect and have a fantastic professionalism towards the club.
"We have a better team than we first thought. All the players are hungry to be involved in this new project at Leeds United."
Benito Carbone, appointed by Cellino as a consultant responsible for "technical and football operations" last month was also delighted with the players' response.
"Fantastic meeting with players today ," the former Aston Villa and Sheffield Wednesday midfielder said on his Twitter account.
"They are all beautiful person, else should how much they love Leeds .. Well done. good start.."
The club has confirmed the players' pre-season schedule will begin on June 26 in Santa Cristina, Val Gardena in Italy.
Meanwhile, Cellino will now focus his attentions on his search for a new coach following the departure of Brian McDermott by mutual consent on Friday night.
Former Chelsea midfielder and Watford manager Gianfranco Zola, ex-Middlesbrough defender Gianluca Festa and surprise candidate Dave Hockaday, who quit as Forest Green Rovers boss last October, have all been linked to the job.