The Belgian club has been trying to sign the forward for weeks and negotiations finally concluded earlier this week.
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Arthur arrived at the Nou Camp from Gremio in his native Brazil for £28 million, and has gone on to make 70 appearances for the club across two seasons.
Mundo Deportivo said Barca have the England international lined up as an alternative to top summer striker transfer target, Lautaro Martinez.
The 31-year-old is deemed surplus to requirements at Old Trafford after 13 years’ service,