Accountancy giant PwC is doing away with landlines at office desks, with all staff expected to only use mobiles by the end of the summer.
The company, which has 24 offices in the UK employing about 18,000 staff, said the switch to mobiles would be "more efficient".
A few landlines will remain for security to use, and in rooms used for client meetings and at reception.
Meeting rooms will use new conferencing technology that can connect to mobiles.
"We already equip all of our people with a mobile phone, and many had already moved away from using their landlines," a spokesman for PwC said.
"With landline usage falling rapidly, we believe that a more mobile-focused policy is a more efficient way of working."
Some small businesses have abandoned fixed-line phones in favour of mobiles in recent years, but PwC's move is one of the first examples of a large organisation doing so.
It comes amid a steep decline in landline use by business.
In 2010, businesses in the UK had more than 10 million landline numbers. However, that number had fallen 35% to just 6.4 million by the end of last year, according to Ofcom.
The amount of time businesses spent talking on landlines has dropped even more dramatically.
In 2010, businesses logged almost 38 million minutes of calls, but that has halved to 18.8 million in 2017.
Residential use of landlines is also in decline. In 2010 UK households made more than 90 million minutes of phone calls, but that had fallen to almost 35 million minutes by last year.
However, most homes need a landline for broadband, so the number of residential lines has actually increased since 2010.
"Because of the pricing structure most people have to have a landline to get broadband - but younger people often don't even plug in a handset," points out James Barford, a telecoms analyst at Enders Analysis.
Earlier this year, BT was forced to cut the cost of a landline by £7 a month for customers that only had a landline.
The price cut came about following a regulatory investigation by telecoms watchdog Ofcom.
It found that although landline rental prices had increased significantly, the cost of providing the services had dropped by more than a quarter.
Ofcom said the hardest hit by the rises were customers, many of them elderly, who had never switched from BT.