The Catalan side announced an agreement with Messi, their all-time leading goalscorer, in July to extend his stay to 2021 but the Argentine has not yet put pen to paper, prompting fears he might leave at the end of the season when his previous contract expires.
In an interview with newspaper Diario Sport, published on Tuesday, Bartomeu said Messi's father Jorge had signed the contract and the only outstanding matter was to take a photo of Messi doing it himself.
"It's all agreed and signed. There are three contracts," said Bartomeu.
"One with the Messi Foundation, which is signed by its president and the player's brother, an image rights contract with Messi signed by his father, who is the administrator of his company, and his employment contract, which his father signed -- he has the power to do so.
"(What remains is) that Leo arrives and we have the official photograph and the protocol of the signature. The contract is signed and it's valid from the month of June, June 30, the same day he got married."
Bartomeu also spoke about Andres Iniesta's new contract, with Barcelona's veteran playmaker on a deal which expires at the end of the season.
"We have the basis of a deal to renew and we hope to seal it in the coming weeks," Bartomeu told Mundo Deportivo.
"The idea is that he has an indefinite contract which renews automatically year on year until he thinks he wants to retire or change."