Shaw, 19, left Southampton in a deal thought to be worth around £27 million in June, signing a four-year deal with Louis van Gaal's team.
And Neville, who made over 400 appearances for United and worked with Shaw at England's ill-fated FIFA World Cup campaign, is excited by what the teenager can offer his former club.
"I am trying to keep guarded here about the size of talent that exists in this footballer," Neville told the Manchester Evening News.
"You are talking about real brilliant potential. The reason United spent £27m on a left-back at his age is because they see the huge talent and I can only endorse that talent.
"You have to watch him at close hand to realise that this is an incredible and hugely talented football player. Luke Shaw is fantastic."
Shaw was picked in England's World Cup squad after a fine season with Southampton in 2013-14, but Neville feels that the youngster will need time to adapt to life at Old Trafford.
"United fans have got to understand, and this is not the boy's fault, is that when you sign someone at that age for £27m, you don't get perfection straight away but you have to give him time and space to develop," he added.
"I think Luke will need time to settle in, as any 19-year-old boy would coming to Manchester. I am expecting he will do well this season but you will really see a really quite fantastic full-back in 18 months to two years.
"When he matures and gets used to the club and settles into the environment and understands the expectation he will blossom.
"I am hoping that, from a football point of view, he is allowed to develop.
"The manager he has now got in Louis van Gaal has a track record of working with young players, so it is all perfect for Luke.
"He has joined absolutely the right football club in terms of his development. He can achieve anything he wants at United. United have signed someone for the long term."
