Cruyff played for Barca in the mid 1970s before returning as coach in 1988 and leading the Catalan club to one European Cup victory and four straight Spanish league titles with a thrilling brand of attacking football.
Guardiola, the midfield linchpin of that side, has eclipsed Cruyff's achievements in his first season in charge by winning the Champions League, Primera Liga and King's Cup, the first treble for a Spanish club.
"Pep and the players have played the best season in the history of Barca and they have demonstrated that they are the best team in history of Barca," a jubilant Laporta said after Barca's 2-0 win over Manchester United in the Champions League final in Rome on Wednesday.
"We have to go back to the Dream Team of Johan and the way Johan transformed football," he added.
"Pep in one year has really created a genius team. It has roots (in Cruyff's philosophy) but at the same time he himself has created something."
Laporta felt the best was yet to come and paid tribute to his board for backing the decision to appoint the untested 38-year-old Guardiola to replace Cruyff's compatriot Frank Rijkaard at the end of last season.
"We thought he was the suitable person for the job and now with much pride and happiness we can say that we took the right decision," said Laporta.
"We have a coach who manages the team majestically, everyone together with a lot of talent and quality and I think it has a long way it can still go.
"It is the prize for perseverance, the prize for those who fought for our ideals."
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Ronald Koeman, the Dutchman who scored the winning goal in Barca's 1-0 European Cup triumph against Sampdoria in 1992, said Guardiola's side was better than Cruyff's.
"We played some good matches back in those days but this is even better," he said in an interview with Spanish television.
Cruyff said Barca's success was down to their constant desire to attack and score goals.
"This Barca side delights everyone who sees it," he told Spanish TV.
"Next year is next year," he added, when asked if Guardiola could repeat the feat.
"You start with zero points and the whole mechanism begins again. It will be a difficult year but Guardiola knows how to get things done."
Guardiola said the club, which now has three European champions titles, was catching up with a select group and that he was fortunate to have learned from Cruyff and his successor as Barca coach Carles Rexach.
"United's stadium is called the Theatre of Dreams and this adds to our prestige having beaten them," he told a news conference.
"We are not the best team in history but we have played the best season in history to win the three titles."
