The deal, approved by Avolon's board, is expected to be completed in the first quarter of 2016.
It has been a fraught battle but one with generous rewards for Avolon's investors, which include private equity groups Cinven, CVC and Oak Hill. Avolon listed last December at $20 a share.
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Bohai was forced to sweeten its initial offer of $26 a share for a 20 per cent stake in July to $32 the following month after an informal rival offer emerged, understood to be from AVIC Capital, a subsidiary of Aviation Industry of China.
The two companies said the agreed price of $31, trimmed by $1, "reflects significant volatility across global equity markets". Bohai had agreed to raise its break fee by $100 million to $350 million, "to provide greater certainty of value and reflecting its commitment to the transaction".
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Denis Nayden, Avolon chairman, said Bohai would bring profile and China relationships to the group. The China market, he said, offers "one of the most compelling growth opportunities in global aviation over the next two decades".
Bohai, which is listed in Shenzhen, is a subsidiary of HNA, which is privately owned and focuses on aircraft, shipping and tourism.
Avolon, one of the world's fastest-growing aircraft leasing businesses, last month reported a better than expected second quarter, recording net income of $55.6 million for the three months to the end of June 30, up 133 per cent compared with the same time last year. Revenue rose 38 per cent to $183.9 million.