The 22-year-old sustained the problem in Manchester United's 3-1 win over Hull City last month, and it was initially feared he could be ruled out of the World Cup.
However, England boss Roy Hodgson included Jones in his 23-man squad and he played in the pre-tournament friendly against Ecuador last week.
And the former Blackburn Rovers man has revealed he breathed a huge sigh of relief when he realised the injury was not going to prevent him from travelling to Brazil.
"Once I did it (injured his shoulder) I thought I might not have a chance, but thankfully it healed quickly and I'm feeling fit, ready and I'm so looking forward to it," Jones told the English FA's official website.
"(The World Cup) was the first thing that came into my mind when I did it.
"I remember getting the scan sitting there thinking 'it might knock my chance'. But, thankfully it's healed nicely and I'm able to be a part of what's going to hopefully be a successful tournament."
Jones partnered club-mate Chris Smalling at the heart of England's defence in the 2-2 draw with Ecuador, and he was thrilled to get back on the pitch after a month out.
"It was nice to get a start, it was a great game, competitive, it was what we wanted and it was great getting 90 minutes under my belt," he added.
"It's been great, the lads were all really keen and excited to get out here and now we're here there's a real belief and buzz about the place.
"It's building up to the first crucial game of the tournament. There has been an awful lot of work that has gone in behind the scenes which most people don't see.
"Everyone is committed, we're in a tight group and everyone's pulling in the right direction for a successful campaign over here."
