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.
Bookmakers Ladbrokes has announced it plans to merge with Gala Coral in a deal expected to value the business at £2.3bn.