The 23-year-old Welbeck, who can play as a centre forward or winger, scored 20 goals in 90 appearances for United and has won 26 caps for England since making his debut in 2011.
"Everyone at Arsenal welcomes Danny to the club and looks forward to his contribution in an Arsenal shirt this season," the team said on its website (www.arsenal.com).
Currently on international duty with England, Welbeck will join up with his new team-mates to prepare for the league match at home to Manchester City on Sept. 13, Arsenal added.
Arsenal did not disclose details, but British media have reported the transfer fee at 16 million pounds.
Manchester United had paved the way for Welbeck's transfer by agreeing to terms on a loan deal with Colombia striker Radamel Falcao from Monaco, British media reported.
(Reporting by Ian Ransom in Melbourne, editing by Nick Mulvenney; Editing by Nick Mulvenney)
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