The bid values NIBC at just over 1 billion euros ($1.13 billion) versus 1.36 billion euros previously.
Blackstone last month cut its original bid by around 25%, to 7 euros per share, after it said the coronavirus pandemic threatened to derail the deal altogether.
NIBC said its board unanimously recommended the new offer, as it said it still offered the best option available for all parties involved.
Majority shareholders JC Flowers and Reggeborgh, which together hold about 75% of NIBC’s shares, have promised to tender their shares at the newly agreed price.
NIBC said it expected the deal to be finalised before the end of the year.
NIBC services around 600 small firms and 400,000 retail clients in the Netherlands and reported a net profit of 194 million euros last year.
($1 = 0.8832 euros)