The 20-year-old midfielder has signed a two-and-half-year contract with the Lilywhites for an undisclosed fee and becomes yet another player to make his way from Old Trafford to Deepdale.
United legend Beckham had a short stint with Preston in 1994/95 while Welbeck, now with Arsenal, spent time on loan in 2010.
"There have been a lot of other permanent signings from Manchester United as well and hopefully this is a good chance for me to come here, play and improve."
He was accompanied by his former United teammate Ben Pearson, who also joined PNE from United this month, on his club journey to Deepdale.
"I have really enjoyed my time at Motherwell and I would like to thank them for giving me the opportunity to play every week," he continued. "It is a great club and I really enjoyed it there. The loan move has really benefitted me.
"I followed Ben's [Pearson] progress as well and it is the same situation; we have gone out and managed to play some league games and now we have got our moves.
"This is a chance to get my career going. It is great to be back home in Lancashire and I am looking to get settled and start to kick on with my career."