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 summer.
"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."