The move will take it past the current high street leader, William Hill, combining Ladbrokes' 2,100 shops with Coral's 1,845.
Current Ladbrokes chief executive, Jim Mullen, will become boss of the merged company, named Ladbrokes Coral.
The two firms had announced merger talks last month.
Peter Erskine, chairman of Ladbrokes, hailed the merger as a "major strategic step for Ladbrokes".
He added: "Together, we will create a leading betting and gaming business. The transaction will provide an attractive opportunity to generate considerable value for both sets of shareholders."
The best way at looking at the challenges facing the merged betting giant of Ladbrokes and Coral is that they have tried to merge before.
In 1998 that planned deal was squashed by Peter Mandelson, the trade and industry minister at the time, on the grounds that it would dominate the industry. Yet at that time the biggest threat to Ladbrokes and Coral did not even exist.
Betfair is the world's largest internet-based betting exchange and it was not founded until 2000.
It is only one of a huge number of online betting companies that pay lower tax bills, can compete for business both here and around the world and face few of the fixed costs of owning thousands of shops on the British High Street.
The rationale behind this merger is to create a company that will stand a better chance of competing with those online giants.
To fund the deal Ladbrokes will offer 93 million new shares to investors, representing 10% of the company.
Gala Coral has been owned by a number of private equity firms, including Apollo Global Management, Cerberus Capital Management, Anchorage Capital Partners and Park Square Capital, since 2010, when it collapsed under £2.5bn of debt.
Under the terms of the deal, those private equity owners will own 48.25% of the new company's shares, with the remainder being held by Ladbrokes shareholders.
Ladbrokes shares closed down 3.3% at 124.1p.
Before the merger talks began, Gala Coral had appointed Morgan Stanley and Goldman Sachs to advise on a possible stock market debut, initially planned for October.
The deal comes just over a week after online bookmaker 888 Holdings won a takeover battle with GVC Holdings for rival Bwin.party in a cash and shares deal valued at about £898m.

Representatives from Highland Council along with Scottish economy secretary Keith Brown and UK minister Andrew Dunlop attended the event.
Announced in March last year, the deal involves direct funding and greater borrowing powers.
There has been criticism that the funding package will not benefit the wider Highland area.
The signing ceremony in Invergordon included an agreement to release £12.25m of funding on three projects.
These are the Science Skills Academy STEMD, which is a a network of "science rooms" to promote learning in science and engineering, and the University of the Highlands and Islands' School of Health, Social Care and Life Sciences.
Also, a land remediation project which aims to make vacant land at Inverness' Longman available to businesses.
Other spending planned at a later date includes about £15m to turn Inverness Castle from a criminal and civil courts building into a tourist attraction.

Family and friends of a young couple had hired the boat for an engagement party and were sailing north of Cairo hit was hit, according to eyewitnesses.
An Interior Ministry statement said 15 bodies had been found and six people were still missing.
The captain of the cargo boat has been arrested. Five people were rescued, but at least two children died.
It is not clear if the couple thought to be celebrating their engagement were among the dead, said AFP news agency.
Traffic had been heavy along the Nile, where many Egyptians had been celebrating the end of the holy month of Ramadan.
Bookmakers Ladbrokes has announced it plans to merge with Gala Coral in a deal expected to value the business at £2.3bn.
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The £315m Inverness City Region Deal has been formally signed off in a ceremony in Invergordon.
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At least 15 people have been killed in a crash between a cargo vessel and a passenger boat on Egypt's River Nile.