BBVA, like rival Santander, is struggling to earn money from more mature markets in Europe and has been expanding in emerging markets, where it sees greater growth opportunities.
Other major foreign banks have by contrast been pulling back from Turkey. Last week UniCredit sold its remaining stake in Yapi Kredi to Kok Holding for 300 million euros.
JP Morgan said in note to clients it expected some share price weakness on the "back of the economic and political risks associated with a larger stake in Garanti."
But the U.S. broker said increasing the stake in Garanti was more accretive in terms of earnings per share than doing a share buyback for 1.4 billion euros, which it said was equivalent in terms of capital impact.
Shares in BBVA fell 3.9%, while shares in Garanti rose around 10% on the news.
BBVA Chairman Carlos Torres tried to dismiss some market concerns, saying on Monday that the lira depreciation and a potential further economic deterioration was "already priced in because the returns are so positive".
BBVA is taking advantage of policy missteps in Turkey, where the central bank has slashed interest rates by 300 basis points since September despite inflation rising to nearly 20% and is expected to cut again this week.
Turkey's lira has weakened sharply in recent months and hit a record low of 10.05 to the dollar.
BBVA has been hedging on the foreign exchange markets to protect its earnings and capital from headwinds in Turkey and bank executives said on Monday it would continue to do so.
ASSETS IN TURKEY AT LOW PRICES
Torres said the deal's entry price in euros was "very attractive", and in lira for the minority shareholders.
Some economists in Turkey expressed concern that recently depreciated assets in the country could now be snapped up at very cheap prices by foreign companies.
"We say that exports are going cheap, tourism is going cheap, housing is going cheap by giving citizenship to foreigners," Mustafa Sonmez, a Turkish economist and columnist, said on Twitter.
"Now, more companies will go to the vultures, with the bank's share at 10 Turkish Lira, getting cheaper in dollars. Garanti is an example of this. It's called total impoverishment (of the country)."
BBVA needs approval from Turkey's Capital Markets Board and the BDDK bank watchdog, government regulators that could technically block the offer.
To cope with the pandemic and ultra-low interest rates, BBVA last year sold its U.S. business, generating more than 8 billion euros to focus on cost cutting in Spain and strengthening shareholder returns.
The Spanish lender's board also recently agreed to buy back 10% of its capital for up to 3.5 billion euros, leaving it with a proforma capital ratio as of September of 13.18, and with an excess capital of around 3.6 billion euros afterwards.
BBVA is expected to give more details regarding additional capital deployments at an investor day later this week.
In the event that not all Garanti shareholders accept the offer though BBVA exceeds a 50% stake, BBVA could increase its holding without launching a takeover bid.
BBVA estimated a maximum negative impact of approximately 46 basis points in the core tier-1 fully loaded capital ratio, and around 13.7% accretion to its 2022 earnings per share and an about 2.3% accretion to its tangible book value per share, assuming all Garanti shareholders accept the offer, BBVA said.
Bank of America advised BBVA on the deal, which would help the Spanish lender generate up to 25% of its earnings from Turkey from 14% at present.
The transaction is expected to be closed in the first quarter of 2022.
($1 = 10.0153 liras)
(Additional reporting by Jonathan Spicer in Istanbul and Emma Pinedo in Madrid; Editing by Inti Landauro, Edmund Blair, Emelia Sithole-Matarise and Catherine Evans) ((email@example.com; +34 91 835 68 32; Reuters Messaging: Reuters Messaging: firstname.lastname@example.org))