The young full-back has recently joined up with the Three Lions squad to train and has committed himself to the country despite having previously represented Finland's Under-21s
The promising defender has a Finnish mother, and has represented the Finland under-21 side, and is therefore ineligible to feature for the senior side until he turns of age.
Jenkinson was recently called up to train with the full Three Lions squad on Sunday to replace Kyle Walker, who is out injured with a calf strain, ahead of their World Cup qualifier with Poland on Tuesday.
With the Gunners right-back now committed to playing for England, the FA can work towards acquiring clearance, so he can be involved in future matches.
Hodgson told reporters: "He didn't take a lot of convincing. We had a problem with Kyle Walker and wanted a full complement in our training session, so we called Carl up. He was in my thoughts anyway.
"I invited him to train with us knowing full well he couldn't take part in this game, but it gave me the opportunity to sit down and ask him the question.
"I don't want to trick him to play for England in a few minutes in a game to block him, but he had to make a decision because we're very interested in him, even if the competition is tougher to get him into the England team rather than the Finland team. He made it very clear he wanted to play for England."