The insurer said it would buy the shares, representing a 2% stake at Orlen's Thursday closing price.
Orlen closed at 53.40 zlotys ($10.78) per share on Thursday, which puts the deal value at 756,2 million zlotys ($1.53 billion).
On Monday, the Polish government cleared the terms of Orlen's planned takeover of Polish gas firm PGNiG and said it would sell 2% of Orlen shares, as part of the merger.
($1 = 4.9554 zlotys)
(Reporting by Maria Gieldon and Karol Badohal; editing by David Evans)