The merger, first announced in September, was unanimously recommended to shareholders by the boards of ADCB and UNB, the banks said in a joint statement.
The tie-up is expected to take effect in the first half of 2019.
It will involve a statutory merger between ADCB and UNB. ADCB will issue 0.5966 shares for every UNB share, corresponding to a total of 1.64 billion new shares issued to UNB shareholders and valuing UNB at nearly $4 billion.
Al Hilal Bank will operate as a separate Islamic entity within the merged bank. Abu Dhabi Crown Prince Mohammed bin Zayed al-Nahyan said in a tweet that the merger would bolster the competitiveness of the UAE's economy.
UAE has 50 commercial banks including 22 local lenders, a number seen as too high in a country of about 9.5 million people.
Saudi Arabia, which has a population of 32 million, has 12 banks and is set to lose two of those if announced mergers are successfully concluded.
"The Abu Dhabi government is continuing its restructuring efforts to create stronger entities with a strong financial base to grow globally," said Tariq Qaqish, managing director of asset management at Menacorp.
Abu Dhabi Investment Council (ADIC), a government investment arm, is the majority shareholder in ADCB and UNB, both listed in Abu Dhabi. Unlisted Al Hilal is wholly owned by ADIC, which is now part of Mubadala Investment Company.
On the date the merger takes effect UNB shares will be delisted from the Abu Dhabi Securities Exchange, with the combined bank retaining ADCB's identity and legal registrations.
The combined entity will acquire Al Hilal Bank for 1 billion dirhams ($272 million) by issuing a mandatory convertible note for up to 117.6 million post-merger ADCB shares to ADIC.
"UNB has a weaker asset quality and much lower profitability than ADCB, and both (of these factors) have been taken into consideration to arrive at the swap ratio," said analyst Chiro Ghosh at Bahrain’s SICO.
"It definitely presents a strong case for further consolidation. We believe banks with similar shareholders have a higher likelihood of merger," Ghosh said. ADCB on Tuesday also reported annual profit of 4.84 billion dirhams, up from 4.28 billion a year earlier.
After completion of the merger, ADIC will own 60.2 percent of the combined bank, other ADCB shareholders owning 28.0 percent and other UNB shareholders holding 11.8 percent.
As reported by Reuters on Monday, Eissa Mohamed al Suwaidi, chairman of ADCB, will retain the same post at the new bank, as will ADCB CEO Ala'a Eraiqat.
($1 = 3.6728 UAE dirham)
(Additional reporting by Maher Chmaytelli; editing by Saeed Azhar and Jason Neely) ((Tom.Arnold@thomsonreuters.com; +97144536265; Reuters Messaging: firstname.lastname@example.org))