Images of the Tottenham defender inhaling the gas earlier this summer were published over the weekend.
Although not illegal, there are health risks associated with the substance, which it appears Walker was not aware of at the time.
These have now been pointed out to the 23-year-old, who has assured Hodgson it will not happen again.
On the eve of England's crunch qualifier in Ukraine, Hodgson made it clear that he has drawn a line under the matter and he is therefore happy for the Tottenham right-back to take to the field in Kiev.
"Yes. I am happy about that," the England manager said when asked about Walker's ability to focus on the Ukraine game.
"He has made his apology. He has made his mistake.
"It was a long time ago, I think he had forgotten about it.
"It might have been worse had it happened last weekend."
The Football Association issued a statement on Monday afternoon confirming that Walker had told Hodgson he would stay clear of the legal high in the future.
"Kyle Walker has expressed his regret for an error of judgement when inhaling Nitrous Oxide earlier this year,'' said an FA statement.
"The FA and England manager have spoken to Kyle about the matter and he has assured us it will not happen again.
"Inhaling Nitrous Oxide is not illegal, but we recognise the associated dangers.
"Kyle has accepted this mistake. He will not face any action under the England Player Code of Conduct."
Walker, like all England players has to abide by a code of conduct brought in by former FA chairman David Bernstein.
The full-back admitted on Sunday night that he made a mistake by inhaling the gas.
"Now I know the health risks, it was poor judgement on my part,'' Walker stated on his Twitter page.
"I won't be doing this again and hope that no one else is influenced into putting their health at risk by my actions."
Walker was named as the PFA's Young Player of the Year in 2012 and has been a regular for Spurs since moving from home-town club Sheffield United in 2009.
He won his seventh cap in Friday's 4-0 win over Moldova and the absence of Glen Johnson and Phil Jones meant he had a clear run at the right-back spot for the game in Ukraine.
"It's important to bear in mind that Kyle is a young lad,'' PFA deputy chief executive Bobby Barnes told Victoria Derbyshire on BBC Radio Five Live.
"Growing up in the public eye, not only will you see successes but you'll also see the mistakes that he's made.
"He is obviously very contrite about this.
"He's made a full apology and more importantly he's made it clear that he's aware of the dangers and he'll transmit that to other youngsters out there.
"The important thing to remember is that he hasn't committed a crime and it's not on the banned list.
"Having said that, it's something that's certainly not desirable for a footballer or a youngster to be doing."