APO•EasyJet shares, which have rallied more than 65% since the initial takeover interest was disclosed, were up 3.6% at 675 pence by 1406 GMT.
The £7.15 per share offer represents a premium of about 81% to easyJet's closing price of £3.94 on May 28, the last trading day before Castlelake's interest became public.
($1 = 0.7424 pounds)
Apollo Global has agreed to buy EasyJet in a deal that values the European budget airline at about £5.70 billion ($7.7 billion), the companies said on Thursday, as rival suitor Castlelake abandoned its pursuit.
The deal ends months of uncertainty surrounding one of Europe's biggest low-cost airlines as the industry grapples with rising costs from the Iran war.
EasyJet's board, advised by Evercore, unanimously recommended the cash offer, saying it considered the terms to be fair and reasonable.
"While we remain confident in the strength of our business and the opportunities ahead, we believe this offer appropriately recognises the quality of the business we have built and delivers immediate, certain and attractive value for shareholders," easyJet Non-Executive Chair Stephen Hester said in a statement.
Apollo, which manages about $1.05 trillion in assets and has previously invested in Sun Country Airlines, Aeromexico and Atlas Air, said it plans to accelerate easyJet's commercial ambitions — including expanding its fast-growing holidays business — under private ownership.
Castlelake earlier on Thursday withdrew from the takeover race without giving a reason.
It had tabled five bids for easyJet before Apollo entered the fray in July, topping Castlelake's £5.5 billion proposal and securing the backing of the airline's board.
Investors and regulators have raised questions about how Apollo will comply with European Union airline ownership rules, given its bases across the bloc. EasyJet's flying rights within the bloc depend on its EU-based airline remaining majority owned and controlled by EU interests.
Following the deal, Apollo anticipates that the family of easyJet founder Stelios Haji-Ioannou and other shareholders remaining invested will hold between 45.1% and 49.9% of the ordinary capital of the purchasing vehicle.
An EU management trust will hold up to 5%, Apollo's funds will hold the rest, up to a maximum of 49.9%.
"Having carefully reviewed the proposal by Apollo, my family members and I have decided to support the recommended acquisition announced by the easyJet board," Haji-Ioannou said in a separate statement.
