Hodgson expressed his relief at the situation having been smoothed over, but stopped short of confirming if he will select Cole for the forthcoming World Cup qualifiers against San Marino and Poland.
Cole apologised to FA chairman David Bernstein after posting an offensive message on Twitter last week.
The Chelsea defender has been made eligible for selection for the two matches, when he could win his 100th cap for England.
But Hodgson has not decided whether he will select Cole or Everton's Leighton Baines for those fixtures.
"The great thing is that we have a lot of players competing for places who have done well when given a chance," Hodgson said.
"It's also interesting that although the game against San Marino looks easier on paper, I know if I leave people out they're going to want to play.
"So it's good to have a selection problem, and more importantly for me I'm pleased the chairman has accepted the apology from Ashley.”
He added: “I know how disappointed he is with the situation and I'm relieved the matter has been totally resolved.
"He (Cole) has played 98 times and hardly ever missed a game when he's been fit.
“He's been regarded as one of the best left-backs in the world for many years, and no-one who is fair-minded could criticise Ashley's commitment to England.
“I'm very happy he hasn't put his position in jeopardy."