The companies confirmed details of the tie-up after revealing the plans last month, marking the latest in a string of deals in the industry as it faces new taxes on online gambling and the need to invest in marketing and technology.
The combined group - to be called Paddy Power Betfair - will have its headquarters in Dublin and is set to maintain a “significant presence” in the UK and Ireland.
They will continue to run separate brands in the UK, Ireland and Italy after the merger, which will see Paddy Power shareholders own 52% of the combined business, with Betfair investors owning the remaining 48%.
But the firms warned of job losses under plans for around £50 million in annual cost savings after the merger.
They said while no decisions have been taken, there was potential for cutbacks in some operational and support functions, which “may involve some headcount reduction”.
The deal - dubbed “Betty Power” in the industry - will bring together Paddy Power’s 336 shops in the UK and 252 stores in Ireland with Betfair’s online betting exchange.
Around 80% of their combined annual revenues will be from online business, making it a force to be reckoned with in the gambling sector as it increasingly moves online.
Gary McGann, chairman of Paddy Power, said: “The merger of Paddy Power and Betfair will create a company of world class capability and people who will deliver substantial up-front synergies and a platform for very exciting business expansion.”
Gerald Corbett, chairman of Betfair, added the deal makes “huge strategic sense by bringing together two industry leading and successful businesses and providing enlarged scale, capability and distinctive, complementary brands”.
Consolidation in the gambling sector has been heating up over the past few months, with rivals Ladbrokes and Gala Coral agreeing a merger in July to create a £2.3 billion gambling giant, which is expected to overtake the UK’s biggest bookmaker William Hill.
The move will bring together 2,100 shops from Ladbrokes and 1,845 from Coral, although the deal is conditional on approval from the Competition and Markets Authority.
And FoxyBingo owner bwin.party last week backed a £1.1 billion cash-and-shares offer from Sportingbet owner GVC after a protracted takeover tussle.
Paddy Power Betfair will be listed in the UK and Ireland and will be headed by Betfair chief executive Breon Corcoran.
He was previously chief operating officer at Paddy Power until he joined Betfair three years ago.
The merged group will have customers from more than 100 countries, with aims for further international expansion across continental Europe, the US and Australia.
The firms confirmed Paddy Power shareholders will receive a special dividend of 80 million euro (£58 million).
Shareholders are expected to vote on the deal in December, with the merger due to complete in the first quarter of 2016.
Paddy Power was founded in 1988 by the merger of three existing Irish bookmakers and it has become well known for its irreverent marketing style.
Its rapid growth in recent years has seen it build more than 300 betting shops in Ireland and the UK, and it now ranks as the third largest online bookmaker and sixth largest online gaming business in Britain and Ireland.
Betfair comes from a newer side of the bookmaking fence.
In 1999, professional gambler Andrew Black and city professional Edward Wray joined forces to form The Sporting Exchange, which went on to launch the Betfair Betting Exchange the following year, offering the market something of a revolution.
Its first market was the Epsom Oaks in 2000, but the new approach to gambling quickly took off by giving punters the chance to take bets and subsequently bet in play.
Betfair floated on the London stock exchange in 2010.