CaixaBank, which is already BPI's biggest shareholder with a 44.1 percent stake, offered to pay €1.329 per share of the Portuguese bank which it does not already own.
The offer is 27 percent higher than BPI's closing share price on Monday and it values Portugal's second-largest listed bank at €1.5 billion ($1.7 billion)
The Barcelona-based bank, one of the most acquisitive banks during the recent financial crisis, said the cash offer was dependent on obtaining the backing of at least 50 percent of BPI shareholders.
BPI must also eliminate an existing rule capping at 20 percent the voting rights of a specific shareholder, CaixaBank said in a regulatory filing.
The buyout will produce synergies worth €130 million a year from 2017, it added.
"It is CaixaBank's wish for BPI to remain a listed company after the completion of the offer and to continue to create value for all shareholders," the statement said.
Portugal's stock market regulator suspended trading in BPI shares to give investors time to analyse CaixaBank's offer.
CaixaBank in August announced in August that it would buy Barclay's Spanish operations for €800 million.
The sale includes Barclay's retail banking, wealth and investment management and corporate banking businesses in Spain and it involved the transfer of the British bank's branches in the country to CaixaBank.
Last year CaixaBank, which bought several ailing savings banks bailed out by the government after the real estate slump, missed out on a chance to buy a local rival, state-owned Catalunya Banc, which was snapped up by BBVA in an auction.
CaixaBank, Spain's third-largest bank after Santander and BBVA, employs more than 31,200 people and has 13.4 million customers.