The fee is believed to be £17m, and on a five-year deal.
The deal was finalised after the 11pm deadline on Monday, with Arsenal being granted an extension by the Premier League to complete the paperwork.
The England international was at Arsenal’s training headquarters London Colney yesterday morning and was watched closely during the morning by a key member of Arsene Wenger's staff.
Video: Transfer deadline day
Welbeck has won 26 caps for England, scoring eight goals.