Hodgson is relieved Cole has made peace with Football Association chairman David Bernstein after his Twitter outburst against football's governing body in this country, whom he described as "a bunch of t****".
Cole has been charged with misconduct and has until Thursday to respond to the charge.
But that controversy seemed a million miles away when Prince William shook hands and appeared to share a joke with Cole when opening the new National Football Centre at the £105million centre in rural Staffordshire.
Cole had helped to smooth the troubled waters after his abuse following the Independent Regulatory Commission (IRC) being critical of his reliability as a witness in the John Terry racial abuse case.
His personal apology to Football Association chairman David Bernstein has been accepted after the England squad met up to prepare for Friday's World Cup qualifier with San Marino at Wembley.
That in turn has prevented a relieved Hodgson facing a selection dilemma over whether to select Cole, who is two caps away from being the sixth Englishman to reach the 100 mark.
When asked about whether Cole will be available to face San Marino, Hodgson said: "It's great to have a lot of players competing for places who have done well when they've had their chance.
"More important is the chairman has gracefully accepted the apology from Ashley. I know how disappointed and saddened he is with the situation.
"I'm quite relieved as an England manager that this matter has been completely resolved."
Hodgson added: "Was Cole's place in jeopardy? The important thing for me was the matter got resolved between the FA and Ashley, the man who made the mistake.
"He's made it very clear he regrets it. He did it in anger. He immediately tried to rectify his mistake, apologised publicly.
"It's just a question of the attack aimed at the organisation represented by the chairman.
"I was always hoping he and the chairman would sort it out between them and I wouldn't have to make a decision of that magnitude. It has been (sorted)."
Hodgson remains convinced Cole is 100% committed to being available for England despite his initial sense of injustice when the findings of the IRC were made public.
He said: "Absolutely. He has the appetite to carry on playing for his country.
"This is a player with 98 caps and who has hardly ever missed a game for England when he's been fit.
"He's been regarded as one of the best, if not the best, left-back in the world for years.
"No-one could question his commitment to the shirt, which makes his contrition the greater, the fact that he might have put his position in jeopardy. I'm glad he hasn't done that."
Hodgson has still to make his mind up whether to select Cole for the San Marino encounter but that would be a decision based on footballing reasons if he is left out.
He is aware of the need to keep players fresh for the more testing challenge Poland will present in Warsaw next Tuesday, while there are also a few fitness concerns.
Midfielder Frank Lampard and skipper Steven Gerrard, who is suspended for the San Marino clash, trained separately from the main squad while striker Jermain Defoe undertook gym work and Cole's fellow left-back Ryan Bertrand missed training with a sore throat.
Hodgson said: "I haven't selected a team for San Marino. I have ideas in my mind. I have 26 players here, one or two recovering with injuries and one who's gone down sick today [Tuesday].
"I may have 22 or 23 but but I know when I make a decision, there'll be some disappointed people even if they do accept I may need fresh people to play against Poland, which is a more tricky game.
"Arguably, anyone I pick from this 22-23 should be good enough to win the game against San Marino because we are sky-high favourites to win that game."