Welbeck, a loan signing from Manchester United, has been sidelined for up to eight weeks after surgery to repair a torn knee cartilage.
The 20-year-old's operation came only one day after Bent stunned observers by completing a move from the Black Cats to Villa.
The injury to Welbeck and departure of Bent leaves Bruce with only one fit striker, Ghanaian international Asamoah Gyan, for this weekend's match away to Blackpool.
"Danny was operated on yesterday and it was confirmed he had a torn cartilage and he will be out for six to eight weeks," Bruce said.
Welbeck sustained the injury during Sunderland's 1-0 win at Aston Villa on January 5, but the problem was initially diagnosed as a hamstring niggle.
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