The 19-year-old departed Tannadice following the expiry of his contract and has penned a three-year deal at Tynecastle Park.
Capable of playing at right-back and as a centre-back in a defensive three or four, Hearts have said they have landed Neilson on a free transfer. Some reports have claimed United will seek compensation for the player.
He made 19 appearances for the Tangerines, while he had a loan spell at Falkirk.
Manager Robbie Neilson spoke of his delight at landing a player he was aware of from his time as United boss.
“Even back then you could see his potential and he’s continued to improve, so I'm delighted that we’ve been able to bring him to Hearts.
“He’s a very quick and strong player with all the attributes needed to make it at the top level, and I’m sure Hearts will provide the perfect environment for Lewis to work hard, develop and take his career forward.”
Sporting director Joe Savage revealed there was an interest in Neilson as soon as it appeared he would be available.
He is the third addition made by Hearts so far this window, joining Alan Forrest and Kye Rowles in committing their future to the club.
“We were interested in Lewis as soon as we heard there was a chance he might not renew his contract at Dundee United," Savage said.
"To get him on a free transfer is great business from our perspective. We're overwhelmed by it, to be honest. At the age he is, with a chance to develop him further. Robbie and his coaching staff raved about him. He's someone that Robbie thinks is very good and that we can make him into an even better player,
“It's good to go down the route of attracting young Scottish players, when we can, it shows that we're committed to our roots of developing footballers. We've done Alan Forrest, and now we've done that with Lewis. We're delighted."