The site, which will house over 400 staff, now has 120 employees on site and started taking customer service calls earlier this month.
The luxury retailer said no decision has been made yet on whether to develop the 10 acres of land it owns in Leeds' South Bank or to maintain the sites it currently owns at Castleford and Keighley in Yorkshire.
Julie Brown, CFO and COO at Burberry, said: "We've made no decision whether to relocate and we don't anticipate any announcement this year. We are certainly maintaining our Yorkshire manufacturing footprint and we are fully committed to the UK."
She was speaking as the firm announced a store closure programme as part of a strategic overhaul that will see it focus its efforts solely on luxury shoppers.
The plans are part of new chief executive Marco Gobbetti's vision for the company, in a bid to sharpen the brand's positioning.
Burberry did not say how many stores it will rationalise or the number of staff affected by the move, but the closures will mainly affect its wholesale arm and will initially focus on the US and Europe.
The opening of Burberry Business Services (BBS) at 6 Queen Street will bring together staff from Burberry’s finance, HR, procurement, customer service and IT teams to simplify processes and teamwork across functions. It has taken over four floors in the building.
Burberry aims to have over 400 roles in the Leeds office by the end of 2018. A small number of these roles have moved from Horseferry House in London, whilst some will be completely new.
Earlier this year Burberry let an option lapse on the Grade I listed Temple Works building in Leeds' South Bank. The firm said it still owns land in Leeds and reiterated that it is committed to Yorkshire.
The luxury fashion brand is considering whether to develop the 10 acres of land it owns next to the building or whether to maintain the sites it currently owns at Castleford and Keighley in Yorkshire. Another option would be to build a new green field site.
Burberry said that one of the considerations during the office location decision process was Yorkshire's connection with universities and colleges. It said it needs a highly skilled workforce which it feels that Leeds offers, with opportunities for graduate roles and apprenticeships.
It added that the historical connection with Burberry and its trench coat manufacturing in Yorkshire marries well with Leeds as a developing centre and a cultural hub.
"Our choice of Leeds underlines our belief in the strong talent available in the North of England and we see it as an attractive destination for our business," said Ms Brown.
It is now looking for talent in the region and sees the local universities and colleges as a very important talent pools in the future.
Burberry said connectivity between its London and Leeds bases will be of the utmost importance and its head office will remain in London.
Burberry said that as it already has two manufacturing sites in Yorkshire (at Castleford and Keighley) and a warehouse in Blyth, Northumberland, it made sense for the group to have an office hub in the North of England.
As part of the store closure programme, Burberry will ditch outlets within department stores and close shops that are not found in or near communities of luxury shoppers.
The announcement comes after Burberry recently confirmed that Halifax-born chief creative officer Christopher Bailey will step down from the board next year, ending his 17-year stint at the high-end fashion house.
It clears the path for Mr Gobbetti to stamp his mark on Burberry, as he also embarks on an ambitious cost-cutting plan.
He said: "Now is the right time for Burberry to implement the next phase of its transformation.
"By re-energising our product and customer experience to establish our position firmly in luxury, we will play in the most rewarding, enduring segment of the market."
The company will take a £15m restructuring hit linked to the store closures.
Burberry made the announcement alongside first-half results, which saw a 26 per cent rise in pre-tax profits to £128m.
Like-for-like sales rose 4 per cent and revenues came in at £1.26bn in the six months to September 30.
"I am pleased with our performance in the half, with strong double-digit underlying profit growth," said Mr Gobbetti.
"Consumers responded positively to fashion and newness, particularly in rainwear and leather goods.
Shares in Burberry fell 9 per cent following the strategy update as investors digested the news.
Steve Clayton, manager of the Hargreaves Lansdown Select UK Growth Shares fund, which holds a 3.8 per cent stake in Burberry, said: "The market is now being asked to back him in a 'no pain, no gain' strategy shift. Early evidence suggests Mr Gobbetti has not carried the crowd with him.
"Mr Gobbetti wants to take Burberry out of all but the most exclusive stores, starting in the US wholesale channel, and then more widely. Product is to be reinvigorated, and accessories emphasised. It's a text-book luxury brand repositioning exercise.
"But this will take time and in the near term, sales growth will be held back and the group must invest more to achieve its goals.
"Shareholders are being asked to accept a couple of years of modest progress, in order to build a stronger proposition longer term."