The defender had entered the remaining months of his previous deal which expired in the summer but ended any doubt over his future, penning a two-and-a-half year contract.
He joins Craig Gordon in committing his future to Hearts.
“I’m delighted that Craig has committed his future to the club,” Neilson told the club's website.
“He’s a big player for us and he’s really come into his own this season with some standout performances.
“To have him around for the next two-and-a-half years is welcome news and I’m sure he and the team will continue to go from strength to strength.”
This season has brought out the best in Halkett since he joined the club from Livingston in 2019.
The 26-year-old has started all but one of Hearts' 25 fixtures this campaign, impressing in the middle of a back three.
No player in the league who has started more than five games has been more dominant in the air than Halkett who has won more than 76 per cent of his aerial duels.
Amongst fans, the player is regarded as one of the most improved at the club this campaign.
Sporting director Joe Savage said it was a “no brainer” to extend his deal with Halkett set to break the 100 appearance mark for Hearts this season, while hinting at further good news for the club.
“We want to keep our best players at the club so that we can continue to progress, and Craig has been a big part of our journey so far,” he said.
“It was, therefore, a no brainer to make him an offer and I’m really happy that there was a keenness from all sides to get it done.
“It’s great news ahead of our return to action, and I’m hopeful that we’ll have even more good news in the coming days.”