Provisional results gave Laporta, a 40-year-old lawyer from Barcelona, 52.57 percent of the votes compared to 31.80 percent for his chief rival Lluis Bassat, a success that theoretically paves the way for Beckham to move to the Nou Camp.
The next two or three weeks will show whether Laporta really can persuade the reluctant Beckham to come to Barcelona or whether he ends up with Barcelona's rivals, Real Madrid.
But the new president can still claim a clear mandate for his far-reaching plans for change.
A win on such a scale in an election that featured six candidates represents a remarkable rise for a man once regarded as persona non grata at Barcelona.
Laporta, by far the youngest of the candidates, is the former head of the Elefant Blau (Blue Elephant) group that campaigned for years against Josep Lluis Nunez, the man who held the post of club president from 1978 to 2000.
Laporta was public enemy number one at Barcelona when he made his first tilt at the Nunez camp in 1998.
Elefant Blau organised a vote of no-confidence in Nunez but despite backing from Johan Cruyff, the club's former star player and highly successful coach, the president survived.
Two years later, Nunez opted not to run for re-election, making way for his long-term vice-president Joan Gaspart.
Laporta decided not to run in opposition, instead hitching his colours to the mast of Bassat, a well-known publicist promising a complete break with the past.
That strategy had little success and Gaspart secured a comfortable win in the vote.
TRAUMATIC SPELL
After a traumatic spell in charge for Gaspart, Laporta this time opted to run against Bassat and gained a huge surge in support with Tuesday's announcement from United that they were prepared to do a deal over Beckham.
Laporta has promised to sign a total of five players with a net investment of 50 million euros ($58.74 million). That is despite Barcelona being at least 100 million euros in debt.
Before the new president can think about signing any players, he will have to attend to other urgent staff matters.
Philip Cocu and Frank de Boer are out of contract at the end of the season and waiting to see if they will be offered new deals, while fellow Dutch international Patrick Kluivert has an agreement to leave the club for a cut-price fee unless the new president agrees to continue paying his huge salary.
There are also question marks over the future of Argentine full-back Juan Pablo Sorin and Spanish midfielder Gaizka Mendieta, both on loan at the Nou Camp.
As for the coach, Radomir Antic signed an extension to his contract under interim president Enric Reyna shortly before elections were called, but that deal is subject to approval by the new president.
Laporta has limited his comments on the subject of the coach to saying he has lined up a world-renowned name. That is likely to spell the end for Antic.
