The 39-year-old has passed the Premier League and Football League's fit and proper person test and will become chairman of the West Midlands side.
He succeeds American Randy Lerner, who bought Villa for £62.6m in 2006.
Villa were relegated from the Premier League for the first time last season, finishing bottom, and have since named Roberto di Matteo as manager.
Dr Xia spent six years at Harvard and Massachusetts Institute of Technology, including five months at Oxford University, before returning to China.
He made his fortune as the owner of Recon Group, a holding company that has the controlling interest in five publicly listed companies on the Hong Kong and Chinese stock exchanges, employing 35,000 people in 75 countries.
His takeover comprises a £52m purchase price and a £24m overdraft. In addition, he will contribute £60m in operating costs.
Dr Xia met the Football League's Shaun Harvey in London on Monday for formal confirmation he had passed the owners' and directors' test, after the Premier League had been satisfied in its investigations.
The new Villa vice-chairman is Chris Samuelson, an international financier who has been involved in a failed takeover at fellow Championship club Reading.
He also attempted to inject finances into Premier League Everton more than a decade ago.
The new chief executive is Keith Wyness, who filled the same role at Scottish Premiership club Aberdeen, then Everton.
Samuelson was instrumental in getting Dr Xia interested in the Villa project and introduced the new owner to Wyness.
Dr Xia is expected to inject about £30m into the transfer fund available to former Chelsea, West Brom and Schalke boss Di Matteo as he rebuilds a first-team squad that won only three league games last season.
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The polls would have been the first electoral contest between the rival Fatah and Hamas movements for 10 years.
Their delay was ordered after lists of candidates for Fatah, which dominates the West Bank-based Palestinian Authority, were cancelled in parts of the Gaza Strip, which is run by Hamas.
Hamas has protested at the court's ruling, describing it as "political".
Fatah said it held Hamas fully responsible.
Thursday's ruling by the high court in the West Bank city of Ramallah came after a Hamas-controlled court in Gaza disqualified several candidate lists drawn up by Fatah on technical grounds.
A challenge was also lodged by a lawyer over the inability to hold the vote in East Jerusalem, which Israel annexed after seizing it in the 1967 war but Palestinians want to be the capital of a future state.
"Elections can't take place in one place and not the other," said the presiding judge.
"The elections can't take place in Jerusalem and its neighbourhoods. Also, there are problems with the formation of courts in Gaza... Therefore, the court decides to stop the elections."
Hamas spokesman Sami Abu Zuhri blamed Fatah for the delay.
"The high court decision is politically motivated and it came in order to rescue Fatah after its lists of candidates collapsed in a number of areas," he told the Reuters news agency.
But Osama al-Qawasmi of Fatah rejected the allegation, saying: "We hold Hamas fully responsible for foiling the election, starting with the unjustified petitions it filed."
The election would have been the first involving Hamas and Fatah since the 2006 poll for the Palestinian Legislative Council, in which Hamas won a majority.
A violent rift with Fatah saw the Islamist movement take control of Gaza the following year.
Although Fatah and Hamas formally agreed a unity deal and a technocratic government in 2014, deep divisions remain, resulting in political paralysis.
Chinese businessman Dr Tony Xia has completed his £76m takeover of Championship club Aston Villa.
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A Palestinian court has postponed municipal elections that had been due to be held on 8 October.