The announcement was made by the Old Trafford club this lunchtime, ending one of the most amazing weeks in their history, which started with hints at unrest and included Rooney's own concerns about the direction United were heading in.
"Wayne has apologised to me and the players," Ferguson told Key103.
"He will also do so with the supporters."
Arsenal manager Arsene Wenger played down the magnitude of the story and admitted his only surprise was at United's initial willingness to make the news public.
"Once the club came out and said they couldn't find agreement, it was a message they wanted to sell," he said.
"There's not a lot to talk about, when a player with 18 months on his contract speaks with his club. The only surprise for me was Manchester United came out and said that.
"It was just a story that for me, from the start to the end, was completely out of interest. When I saw headlines I just turned the page."
Former United player Clayton Blackmore felt Wayne Rooney had to apologise.
He said on Sky Sports News: "He came out with a few things, saying the squad wasn't good enough and the ambition wasn't there. But the ambition's always there.
"I think he knew he had to apologise and I think everything will be swept under the carpet now and carry on where we left off about a month ago, before it all started."
Blackmore claimed the episode showed how influential Ferguson is.
"It think it just shows how strong and how powerful the manager is," he said.
The former Wales international added: "Things like this, when it looks like we've lost him and things have gone too far, now they've gone back together, it could work even better for us.
"Wayne could end up being an even better player, you just don't know."
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