Solskjaer signed a three-year contract to take charge at Old Trafford last week, having enjoyed a successful three-month caretaker spell.
The Norwegian took three points from his first game as full-time manager, with United earning a hard-fought 2-1 victory over Watford.
Solskjaer has transformed the mood around the club since replacing Jose Mourinho in December and Jones thinks the sense of optimism can last for a while yet.
The 27-year-old, who impressed while making his first Premier League appearance in almost two months on Saturday, was signed by Ferguson in 2011.
Ole Gunnar Solskjaer: The games that got him the job
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And he feels former United striker Solskjaer has restored the confidence and self-assuredness associated with the Scot’s time in charge.
“I definitely I feel the same sort of vibe about the place,” Jones said after Saturday’s win.
“The same... the same buzz. The same... I don’t know, like you can’t really put your finger on it, but I know exactly what you’re saying.
“You can see similarities in that stage between now and back then. It’s nice, it’s refreshing and we’re all enjoying it.”
Though Solskjaer’s appointment has generally been received well, some have questioned the decision to confirm him as manager before the end of the season when much is still to be decided.
Before beating Watford, United had lost consecutive games under the Norwegian for the first time and the fabled ‘new manager bounce’ appeared to have worn off.
Jones, however, does not believe that the timing of the decision will have much an impact on the remainder of United’s campaign.
“It didn’t matter whether it was last month, this month, next month, end of the season,” he said. “I think we understand exactly what he wants, what he wants from us and vice-versa and it works.
“The players are enjoying their football. It’s exciting, we’re moving in the right direction. We’ve got some great footballers here. We want to learn and improve and get better and we will do.”
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