The Manchester United midfielder told the Football Association he did not want to be selected for Euro 2012.
However, he has now made himself available and comes into a squad that sees Tottenham duo Steven Caulker and Jake Livermore selected for the first time, in addition to Chelsea's Ryan Bertrand.
England captain Steven Gerrard, plus established regulars Wayne Rooney and Ashley Cole, were left out of the squad for Wednesday's match in Berne but Frank Lampard - who missed Euro 2012 through injury - has been included.
Hodgson has retained just three players who started the Euro 2012 quarter-final defeat to Italy in Kiev; Manchester City duo Joe Hart and James Milner, plus Ashley Young, who missed in the shoot-out defeat.
Other than Hart, Lampard looks the most likely skipper.
Goalkeepers John Ruddy and Jack Butland are the other uncapped members of Hodgson's squad, in addition to Tom Cleverley, who would have made his debut 12 months ago had the friendly with Holland not been postponed due to the London riots.
The England squad meet in Watford on Sunday evening, although Butland will be released back to Birmingham on Tuesday as they have a League Cup tie against Barnet.
In total, 10 of the players who went to Euro 2012 have been picked, while five members of Stuart Pearce's Olympics squad are also involved.
Micah Richards and Phil Jones are among the group not considered due to injury.
Hodgson claimed he had been under the impression Carrick had turned his back on England for good.
However, following talks with the United midfielder, it now transpired that was not the case.
"Michael Carrick would have always been in our thinking," Hodgson told Sky Sports.
"I was given to believe he didn't want to be part of the England set-up. He didn't want to be considered for the Euros so I reluctantly thought if people are not available they are not available.
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"He has had discussions with Gary and me since and it turns out that he does want to play. This is an ideal opportunity to invite him to come and play for England again.
"There has never been any doubt that Carrick has not been in our thoughts or our wishes. It was more a case of believing he wasn't available for England and it was a final decision."
Hodgson also emphasised Terry's absence had nothing to do with the FA charge currently hanging over him as a legacy of that clash with Anton Ferdinand at Loftus Road in October.
Ferdinand's brother Rio is facing a different charge and he was not included either. However, Hodgson said he will consider both men in the future.
"John Terry has been through a charge in a court, now he has to go through the process the FA have embarked upon," said Hodgson.
"The same applies to Rio. As far as I am concerned, it is a disciplinary matter, which the FA will take care of.
"As long as they don't suffer enormous bans that will keep them out of my thinking there is no reason for me to believe I can't consider them in the future. And obviously I will."