ESPN Brazil reports that the agreement came after the player put pressure on Liverpool to let him leave.
The Brazilian is now set to join Barca for a base fee of €90 million (£81.6m), with bonuses that could bring the deal to €120m (£108.8m).
Yesterday a delegation from Barcelona headed up by chief executive Oscar Grau travelled to finalise the negotiation.
The Brazilian midfielder told Liverpool earlier on Monday that he wanted to leave and join Barcelona.
Barcelona’s interest in Coutinho predates Neymar’s move to Paris Saint-Germain.