That is according to club president Josep Maria Bartomeu.
Speculation has been rife regarding the future of the Argentine, with reports claiming the forward was unhappy after a turbulent summer.
However, Bartomeu has insisted for some time that a deal is in place and official confirmation will be released soon.
And the Barca chief now claims Messi is already playing under the terms of a new deal, which is set to expire in 2021.
Speaking to 8TV, Bartomeu said: “We will take the photo with Messi’s signature, hopefully before the end of the year.
But the contract has been signed by his father, who has the power of his image rights.
“This contract is signed until 2021 and he is already playing under it.”
The five-time Ballon d’Or winner has started the season in fine form, scoring eight goals in all competitions.
His Barca side swept past Juventus 3-0 in the Champions League on Tuesday.
The Italian side have been linked with Messi’s long time team-mate Andres Iniesta. But it appears the midfielder is also close to agreeing a new deal.
Bartomeu said Iniesta is set to stay, adding: “The agreement with Iniesta will be special, it will be different just because it is him.
“I won’t reveal exactly what because it is part of private negotiations, but with Ramon Sostres, we have been talking for a long time.”