Jones joined United from Blackburn Rovers for a fee thought to be in the region of £16.5 million after spurning the advances of the Anfield club.
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The 19-year-old only made his Premier League debut in March 2010, but racked up 25 appearances last term despite not playing until December due to a cartilage operation.
However, his performances in helping Rovers stay in the top flight were enough to convince Sir Alex Ferguson to make him his first signing of the summer.
Speaking exclusively to FourFourTwo.com, Lawrenson was full of praise for Ferguson's young recruit, comparing him to Chelsea skipper Terry.
“I hate that sort of line when they say ‘oh yeah he’s the new such and such’,” Lawrenson said.
“But what I will say is that Jones reminds me a little bit of John Terry in the way that he plays.
“Fergie’s kind of looked at that position - with Chris Smalling also at the club - and thought, ‘I’m good now for five-10 years'. They've also got Jonny Evans, who isn't even in their top four centre-backs.
“But I think United have always thought, ‘look we’ll worry about the team when we need to pick the team’. If you have to leave people out like [Dimitar] Berbatov, like Smalling and Jones and one of the Da Silva boys or whatever, you just leave them out.”
Jones joins fellow centre-backs Rio Ferdinand, Nemanja Vidic, Smalling and Evans at Old Trafford, but Lawrenson does not believe the strong competition to be a problem.
He expects the England Under-21 international to get plenty of playing time with United, either in defence or possibly In the centre of the park.
"I think if they're all fit then you'd have to be a hell of a player to be in front of Ferdinand and Vidic,” he explained.
“But Rio doesn’t play that many games. Also, they've got the question of Smalling, he’s already a very, very good player.
“I think they’ll just look at Jones - Fergie might even sometimes use him in midfield - but I think he’ll try and play him as often as they can.
Pundit Mark Lawrenson was talking about the forthcoming season at the Kinect Sports for Xbox 360 football event at the Sports Café, Central London
By Joel Lamy
