The Premier League have confirmed that Manchester City striker Benjani has completed his switch to Sunderland.
The Black Cats blamed communications problems for their failure to confirm the capture of the Zimbabwe international before Monday's 5pm transfer deadline.
Boss Steve Bruce had hoped that 'common sense would prevail' and that now appears to be the case.
Benjani has struggled to break into the first-team picture during two years at Eastlands, but Bruce is a big fan of the 31-year-old former Portsmouth striker.
He had said after Monday's goalless draw with Stoke City: "We had huge, huge difficulties with email and faxes so we hope a little common sense prevails.
"I think we've lodged everything in time, we've done everything we possibly can and I'm convinced we had everything in in time.
"The paperwork was lodged but we had some huge, huge difficulties and we informed both the Premier League and the FA at the time of those.
"We wait to find out but I hope we are granted the player, who would be a huge boost to us."