LaLiga announced the private equity firm will acquire a 10 percent stake in a new business that will take control of most activities, with the focus on commercial ventures.
The deal, which values LaLiga at €24.3billion, was approved unanimously by the executive committee and is set to be proposed to the general assembly.
However, both Barca and rivals Real Madrid have denounced the proposal, citing concerns over what impact the tie-up will have on television rights.
Laporta aired those concerns himself on Friday when speaking about Lionel Messi's departure from Camp Nou, the club president unwilling to risk Barcelona's long-term future simply to make sure their star player stayed put.
LaLiga president Tebas was clearly watching on and, during the media conference, wrote on Twitter: "Hello Joan Laporta, you know that the CVC operation does not mortgage the TV rights of Barcelona for 50 years, what it does is that they have more value for all the clubs and so you can MORTGAGE your BANKS and solve the great debt. So you understood hours ago."
LaLiga, which controls the top two divisions in Spanish football, have said 90 per cent of CVC's €2.7bn investment would be earmarked for its clubs.
Still, the added income was not enough for Barca to keep hold of Messi, who now faces an uncertain future. His departure will be a blow for LaLiga too, considering his global appeal.
Laporta responded when Tebas' tweet was brought to his attention by a journalist, professing his belief that the value for 10 per cent was too low.
"Hello, Javier. I will tell you that we do not interpret it that way," Laporta said.
"In fact, yesterday our senior executives spoke with those who run this operation and they have not given us satisfactory answers. I understand the legal formulas that you articulate, because they are ingenious, but this implies giving up a part of our rights with a horizon of half a century.
"In addition, I would tell you that the amount set by CVC is much lower than what, for us, the 10 per cent of LaLiga should be valued. With all my love, I have already answered you."
Tebas duly returned serve on social media, referencing Barcelona's involvement in the European Super League proposal that failed to gain traction.
He wrote: "You recently said that we were broke. Now that we are valued at €24.250million and there is access to partners TO GROW, you are concerned about the future income of LaLiga that you gave up for dead. You are proven wrong."
Barca's perilous financial predicament means they have not yet been able to register new signings, including Memphis Depay and Sergio Aguero.
The club's official statement on the CVC agreement read: "FC Barcelona feels it is inappropriate to sign a half-century agreement given the uncertainties that always surround the football world.
"The terms of the contract that LaLiga is describing condemn FC Barcelona's future with regard to broadcasting rights.
"FC Barcelona wishes to express its surprise at an agreement driven by LaLiga in which the teams' opinions, including those of FC Barcelona, have not been taken into account.
"There has not even been a presentation of options offered by other competitors in order to evaluate the pros and cons in a post-pandemic situation in which there are still many questions that are left unanswered."