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The 44-year-old Vilanova had a tumour removed from a salivary gland in his throat in November 2011 and in December 2012 he suffered a relapse.
He underwent surgery again followed by 10 weeks of chemotherapy and radiotherapy in New York.
Vilanova returned to the helm of Barcelona in March and led the club to the Spanish league title.
"After evaluating the results of routine rests this week Tito Vilanova has been presented with the option of carrying out a treatment to continue to control his illness which will make it incompatible to carry out the role of first team coach from now on," Rosell told a news conference.
"I want to ask everyone, especially the media, in the name of his family to show the maximum respect for the privacy of the whole process which will start now," he added.
Vilanova's replacement will be announced "probably in the beginning of next week," Rossll said.
Vilanova replaced Pep Guardiola as manager in June 2012, having previously worked as his assistant.
However, after an amazing start to his first senior managerial role on the field as Barcelona made the best ever start to a Spanish league campaign, the club was rocked by the news in December last year that the cancer had reappeared.
Vilanova had surgery on a salivary gland and then spent two months in New York receiving chemotherapy treatment before returning to the touchline for Barca's Champions League quarter-final tie against Paris Saint-Germain in March.
Having amassed a commanding lead in the first-half of the season, Barca comfortably went onto to seal their 22nd Spanish league title in May, but a draining season on and off the pitch seemed to have taken its toll on the squad when they were hammered 7-0 on aggregate by Bayern Munich in the Champions League semi-finals.
Despite that defeat Vilanova continually stressed that had the energy and determination needed to continue in the role for the upcoming season.
"I feel fine. I have the energy and the desire to continue at the head of the team next season," he said.
But unfortunately his health once again failed him and he has now agreed to step aside to concentrate on his battle with cancer.
Like many of the world's best coaches, Vilanova made it to the top despite not having a distinguished playing career himself.
He started off in Barcelona's ranks as a youth player where he first met Guardiola, but moved on after failing to break into the first team and only very briefly featured in the top flight with Celta Vigo between 1992 and 1995.
After working as a coach and technical director respectively at Catalan sides FC Palafrugell and Terrassa though, Vilanova was called upon by his old friend Guardiola to form part of the coaching staff at Barcelona B after Guardiola had been appointed as manager in 2007.
After a season working with the club's youngsters, Vilanova followed Guardiola as he graduated to first-team boss the next season and was a key part of the side that won 14 trophies over a remarkably successful four-year period.
"I am not looking to compare myself to anyone; I simply want to do my job," said Vilanova when he was officially presented as the new Barca coach in July 2012.
Vilanova's relationship with Guardiola appeared to have cooled since the latter's decision to leave Barca last year.
The new Bayern Munich boss claimed last week that the current Barca board, led by president Sandro Rosell, had deliberately tried to Vilanova's illness to damage Guardiola's reputation by claiming he had not visited his ailing friend despite living in New York where Vilanova was undergoing treatment.
That claim was flatly rebuffed by Vilanova last week, who said he had only seen Guardiola once during his two-month spell in the American city.
Barcelona's focus throughout Vilanova's struggles have quite rightly been focused on his health rather than the state of the side on the pitch, however his departure does now leave one of the world's leading clubs without a permanent manager less than a month before they are due to start the defence of their La Liga title.
