Messi, 33, voted in Sunday's election as Laporta saw off competition from Victor Font and Toni Freixa to return to the post he previously held between 2003 and 2010.
More than 55,000 club members participated in the vote, a turnout of just over 50%, with 30,184 of them voting for Laporta to set up champagne-soaked celebrations inside his campaign cabin at Camp Nou.
It was the first time Messi has voted in an election -- they usually take place in the summer when he is on international duty -- having been very critical of the club's previous president, Josep Maria Bartomeu, when he tried to leave last summer.
With Messi's contract expiring in June and his future still up in the air, Laporta said the fact he chose to exercise his right to vote suggests he's leaning towards staying at Barca under his presidency.
"It was really nice seeing Messi go and vote," Laporta told reporters on Monday. "It is more proof that he loves Barca. I am convinced that he wants to stay. And yes, he has already congratulated me for winning."
Throughout his campaign, Laporta reiterated that of the three candidates he was the most likely to convince Messi to remain at the club.
The forward wanted to leave the club last August but was blocked by Bartomeu's board. With Manchester City and Paris Saint-Germain showing interest, Messi said he will wait until the end of the season before making a decision.
Manchester City coach Pep Guardiola was also among those to congratulate Laporta, posting a message on social media. Laporta was the president that appointed Guardiola as Barca boss in 2008 and he has always said the door will remain open if he ever wants to return.
Meanwhile, Laporta has begun work on restructuring Barca off the pitch.
Former Valencia general manager Mateu Alemany will take on a similar role at the Catalan club, while sources have confirmed to ESPN that Jordi Cruyff, the son of Barca legend Johan, is likely to come in as sporting director.
Cruyff is head coach of Chinese Super League club Shenzhen FC but is expected to leave that position and it is possible that he flies into Barcelona later this week.
Barca's first game since Laporta was elected is against PSG on Wednesday in the Champions League, when they must overturn a 4-1 first-leg defeat.
In the middle of the celebration on Sunday, Laporta screamed "to Paris to see if we can produce another remontada [comeback]" in reference to Barca's 6-1 win against the French side in the same competition in 2017.