The Spanish and European champions will repurchase Bojan at the end of the 2012/13 season for 13 million euros unless Roma decide they want to keep him, the La Liga club said on their website on Friday.
In that case, the Italian club will have to pay another 28 million, Barca said.
"The buyback clause can be blocked by AS Roma but in that case the total cost of the transfer would be 40 million euros," they added.
The structure of the deal reflects Barca's desire to keep their options open when it comes to holding on to promising players who have come through the club's famed youth academy but are not getting much playing time with the first team.
The 20-year-old Bojan, who said at an emotional farewell news conference he was unhappy with the way coach Pep Guardiola had treated him, joined the Catalan club's boys team in the 1999/2000 season.
He made his first-team debut against Osasuna in September 2007 and the following month became the Barca's youngest scorer in La Liga with a goal against Villarreal at the age of 17 years 53 days.
The baby-faced striker has won a host of trophies over the past three seasons but is not one of Guardiola's first-choice forwards and has spent most of the time on the bench behind Lionel Messi, David Villa and Pedro in the pecking order.
He will join up with former Barca and Spain midfielder Luis Enrique, who has moved to the Italian capital to take charge of Roma after a successful season coaching Barca's B team.
POSITIVES REMEMBERED
At a news conference attended by team captains Carles Puyol and Xavi and sporting director Andoni Zubizarreta, Bojan said he was hoping to rediscover the joy of playing.
"As a fan and club member I believe Pep is the best coach Barca could have," he said.
"But as a player there are things I do not agree with and which I felt very bad about."
He added that not playing in Barca's Champions League final victory over Manchester United in London in May had been painful, particularly as he was also left out for the 2009 final in Rome.
"There was not much confidence shown in me. I wasn't given the continuity needed to show what I can do," he said.
"But I am also aware that I am privileged to have been part of the first team, of a magnificent team that has made Barca into the world's best.
"For that reason I am not leaving with feelings of hurt. I will remember the positives."
Bojan scored 41 goals in 163 appearances for Barca, 26 in the league, nine in the King's Cup, five in the Champions League and one in the Spanish Super Cup.
