The Spain international, who has just arrived in Brazil with the world and European champions for the Confederations Cup, has rejected the chance to renew his deal with the La Liga champions beyond 2014.
The 31-year-old has said he would like to experience different leagues and cultures after almost a decade as Barca's number one choice, which raised the possibility of him leaving during the closed season.
"Victor Valdes's representative has officially told [sports director Andoni] Zubizarreta that the player will complete his contract," Rosell told a news conference, as he reviewed the club's season.
"We are delighted he will be with us next year."
A long-term replacement will still be required for Valdes, with reserve keeper Jose Manuel Pinto aged 37, but Rosell was not specific when he spoke about possible reinforcements beyond Brazil forward Neymar.
"I believe we will sign one or two more players," he said. "That also depends on whether players leave."
The club has been rocked by the news on Wednesday that their World Player of the Year Lionel Messi and his father have been accused of tax fraud related to image rights by the Spanish tax authorities.
The prosecutor's office for tax crimes in Catalonia has accused them of filing fraudulent tax returns for the years 2006 to 2009 and of owing more than four million euros.
Messi, who is due to play for Argentina in a friendly in Guatemala on Friday, has denied wrongdoing, and Rosell backed the club's leading scorer.
"Messi's family is quite calm about it," he said. "They have our support. I have no doubt about his innocence."
