The 19-year-old joined the Old Trafford outfit from Blackburn Rovers for £16.5 million earlier this summer, having made just 35 Premier League appearances for the Ewood Park side.
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Jones did not link up with his new team-mates immediately having taken part in the European Under-21 Championships in Denmark, alongside fellow United stopper Chris Smalling.
But the youngster has stated that he is now starting to adapt to his new surroundings, having initially been star-struck following the news that Sir Alex Ferguson was keen on recruiting him.
"It's just sunk in. It took a while to sink in but I'm delighted to be here," he said in The Sun.
"It's a massive club, the best club in the world possibly, and I'm just happy to be here.
"I was away on holiday with my girlfriend when I got a phone call from the boss saying he was interested and things progressed from there.
"It was an unbelievable feeling. I picked the phone up and he says, in his Scottish voice, 'It's Sir Alex'. It's what anyone dreams of, for that phone call to happen.
"I think the lads have been brilliant and have made me feel very welcome, so I feel settled.
"I still live with my family, I'm still 19 and it's happened at quite a young age but I'm just enjoying it. They keep me grounded and make sure I stay focused."
Jones made his United debut, as did goalkeeper David de Gea, in the club's 3-1 victory over Chicago Fire at the weekend.
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