The England striker said he wanted to leave the club, only to change his mind.
Rooney signed a new five-year deal on Friday just two days after saying he wanted to move elsewhere.
Ferguson said in the match programme for Tuesday night's Carling Cup match with Wolves: "It's been a traumatic time for Manchester United and no doubt everyone is as relieved as I am that the situation with Wayne Rooney has been resolved.
"We're delighted that he'll remain with us and he'll play a key part in our challenge for silverware on all fronts - both this season and in the years to come.
"Once the news came out that Wayne wanted to leave, the publicity and impact that had, and the response it generated, showed how big Manchester United is and that resonated with him quite a lot.
"Wayne apologised to me and the players and it's now time to draw a line under last week and face the challenges that lie ahead.
"We have a good squad, the unity and spirit is fine and the structure of the club is good. There is nothing wrong with United."