The 18-year-old, whose previous deal was due to expire at the end of this season, made his senior debut at 16 against St Mirren in May 2013 and has gone on to make 38 appearances for the first team.
He has also been capped nine times for Scotland at under-21 level after being fast-tracked through the youth ranks in the national set-up, captaining the side in a 1-1 draw against Switzerland last November.
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Sunderland are thought to be long-term admirers of the classy defender, while Serie A champions Juventus were credited with an interest in the player in 2013.
However, he has now agreed a deal which will keep him in Gorgie until the summer of 2017.
McGhee’s new contract represents a massive boost for the capital club ahead of tomorrow night’s mouth-watering Championship showdown against second-placed Rangers.
Neilson said: “Jordan is one of the top prospects in the Scottish game. It is good to get his future tied down and this gives him time to develop.”
McGhee tweeted: “Delighted to have signed another deal at Hearts, looking forward to the next few years ahead.”
Meanwhile, Neilson admits he faces a selection headache for the trip to Ibrox as he ponders who will spearhead the Jambos attack. Genero Zeefuik, a loan arrival from Eredivisie outfit Groningen last week, enjoyed a scintillating debut for the capital club against Dumbarton, netting a predatory double – albeit he blew his chance for a hat-trick by missing a late penalty.
The burly Dutchman led the line with James Keatings at the Bet Butler Stadium and, although the former Hamilton forward failed to find the target, he boasts an impressive tally of four goals in his last six games.
Neilson has also been buoyed by the return of Osman Sow, who was the hero when the sides last met in Glasgow by scoring a 93rd-minute winner in a 2-1 triumph, and Dale Carrick to training this week.
He said: “Osman and Carrick are back training so the options are there. I’ll need to have a look at it for Friday and make a decision about what we want to do.”
Neilson is still weighing up whether to employ one or two strikers at Ibrox, after admitting his side lost impetus following the withdrawal of Zeefuik against Dumbarton.
Hearts have fielded one up front in each of their two wins over Rangers this term, Sow in Govan and Soufian El Hassnaoui at Tynecastle, and Neilson insists his side are tactically flexible as the seek to open up a 16-point gap at the summit of the Championship.
He added: “Having two up front makes a huge difference to us. When we took Genero [Zeefuik] off against Dumbarton, we went back to one up top and we couldn’t quite get back in again.
“We managed to start creating more chances when we reverted back to two. It’s definitely the way we want to play but there are certain games where we have to change it.”
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