The office building had been owned by the Royal London Mutual Insurance Society but was put on the market for £40m in October.
The Grade I listed property has the two famous Liver Birds on its roof.
Along with the Cunard and Port of Liverpool Buildings, it is one of the Three Graces on the city's waterfront.
The 330,000 sq ft (31,000 sq m) building is currently home to companies including ITV and HSBC.
Thomas Landschreiber, chief investment officer of Corestate, said the company is looking to "invest significant funds to maintain and strengthen this city-building office building in the long term".
"As a new owner of this emblematic building, we appreciate its heritage and its importance to the people of Liverpool," he added.
Source: Museum of Liverpool

Sheffield Wednesday's Chris Kirkland, 31, required treatment after being struck in the face during Friday's game against Leeds United at Hillsborough.
Leeds fan Aaron Cawley, 21, from Cheltenham, Gloucestershire, pleaded guilty at Sheffield Magistrates' Court to assault and entering the field.
He was given a 16-week jail sentence and a six-year football banning order.
Leeds United said the club intended to ban him from its Elland Road stadium for life.
Kirkland, who has played once for England, was shoved in the face and fell to the ground moments after conceding an equaliser in the 76th minute of the match at Hillsborough, which finished in a 1-1 draw.
The court was told that Kirkland made a victim impact statement which said: "I feel shocked, upset and angry.
"I think the man is a thug and should be caught and put in jail. Anyone who supports what he's done is just as bad."
The court heard Cawley had been drinking heavily and had already breached two previous banning orders.
Prosecutor Paul Macauley said Cawley told police he had drunk a number of cans of lager and three-quarters of a litre of vodka before arriving in Sheffield and then had a further seven to 10 pints of cider.
Mr Macauley said he was "so drunk" he did not remember what happened, and only realised after seeing the footage.
District Judge Redhouse heard that Cawley emailed the police to say sorry and also emailed Sky Sports, which broadcast the match, in the hope his apology would be passed on to the two clubs and Kirkland.
A spokesman for Leeds United said: "We are pleased to see the matter dealt with by the courts so quickly.
"The club will also ban the individual for life from Elland Road when this banning order expires.
"While we are pleased to see justice brought so quickly, our one disappointment is that we feel the sentence could, and should, have been considerably longer."
Writing on Twitter, Angela Smith, the Labour MP for Penistone and Stockbridge, also criticised the sentence.
The MP, a Sheffield Wednesday fan, wrote: "16wks prison sentence for assaulting a goalkeeper & breaching a banning order? I am quite frankly astonished! #justicenotdone."

These are the words of judge Karin Jung, who gave two 1860 Munich fans the choice to buy Bayern merchandise for a fan they attacked - or spend 15 months in jail.
The defendants, who refused to name a third person involved when they ripped the jacket, shirt and straw hat off the Bayern fan last year, opted for the pride-swallowing trip to the rival club store.
"I thought about what would be really painful to them, and doing something like this really bothers this type of people," Jung - who got the victim's consent for the quirky sentence - told Bild newspaper.
This was no cheap shopping trip though as according to their lawyer, the accused parted with around £350 each in compensation as well as handing over a Bayern hat, scarf and jersey in court.
Liverpool's iconic Royal Liver Building has been sold for £48m to Luxembourg-based real estate investment manager Corestate Capital Holding.
[NEXT_CONCEPT]
A man has been jailed for running on to the pitch and attacking a goalkeeper during a Championship football match.
[NEXT_CONCEPT]
"I wanted to show that football is football and not a battlefield."