Off contract from Olympique Lyon at the end of this month, Depay featured in Holland's victory over Euro 2020 opponents Ukraine on Sunday.
Mundo Deportivo says talks between Barca and Depay's minders have been maintained over recent weeks and on Monday a final exchange of contracts were made.
Depay was running a final check of the forms on Monday afternoon and there is a confidence that Barca will be able to announce his commitment in the coming days.
Barca coach Ronald Koeman was informed on the weekend that Depay would be joining his squad for the new season. Koeman has been eager to add Depay to his Barca squad since his appointment last summer. The pair worked together while Koeman was in charge of the Netherlands national team.
Last season, Depay played 40 games for Olympique Lyon, scoring 22 goals and producing 12 assists.
- updated June 16