Vonovia said it was offering 9.56 billion Swedish crowns ($1.08 billion) for Victoria Park, which owns 14,000 units in Stockholm, Gothenburg and Malmo
Low interest rates have fuelled interest in real estate among investors searching for higher returns and companies looking to bulk up.
Since going public in 2013 Vonovia has grown into Germany's biggest residential property company by swallowing up smaller rivals and has expanded outside its home market, snapping up Austria's Conwert and Buwog.
The German firm said it was attracted by Sweden's regulated rental market and a fragmented housing sector ripe for consolidation.
"We are very excited about entering the Swedish market for the first time, and we are particularly happy that we identified Victoria Park as a company that follows the same business principles," Vonovia CEO Rolf Buch said.
Despite increased competition for portfolios, Buch said he expected rising demand for apartments as people flocked to big cities to support prices and rents, especially in Germany and Sweden where there remained a lot of catch-up potential.
Vonovia said its offer represented an 11.8 percent premium to Starwood's rival offer, which valued the company at roughly 8.68 billion crowns.
Buch told journalists he was in "good talks" with Starwood and that it would not come to a bidding war. Victoria Park's board had recommended shareholders reject Starwood's approach, saying it did not reflect the company's value. On Thursday, its bid committee voiced support for Vonovia's offer.
Investors representing 37 percent of Victoria Park's voting capital have agreed to accept Vonovia's offer, it said. The offer runs until around June 18, and was contingent on securing more than 50 percent of voting shares.
Vonovia, which is offering 38 crowns in cash for Victoria Park's common shares, after the market close raised 995.8 million euros in a placement of 26 million new shares, funds which it said would be used in connection with the takeover.
Victoria Park closed up 9.7 percent at 38.50 crowns while Vonovia's stock closed down 2.6 percent at 40.81 euros.
Sweden has been an attractive property market for the past two decades, as property prices rose quickly, fuelling fears of a housing bubble. But prices have dipped in recent months on a surge in building and tougher mortgage repayment rules aimed at curbing high household debt.
Vonovia's latest foreign venture is part of a European expansion drive. In March, it completed a 5.2 billion euro deal to buy Austrian peer Buwog and has flagged interest in further cross-border acquisitions in Sweden or the Netherlands.
Rules forbidding listed companies owning social housing remain an obstacle to its ambitions in France.
Rival Starwood has also been seeking to expand, making offers for minority stakes in Austria's CA Immo and Immofinanz as it seeks assets in central and eastern Europe. Immofinanz has rebuffed Starwood's offer as too low.
Vonovia's Buch said he believed listed companies would have the upper hand over private equity because of their scale and lower cost of capital.
Separately, Vonovia also reported results for the first quarter and raised its 2018 guidance for funds from operations (FFO 1), a measure of recurring free cash flow, to 1.03 billion to 1.05 billion euros from 960 to 980 million euros.
It said it expected the Victoria Park deal to be accretive to core profit by 2019.
(Additional reporting by Hans Seidenstuecker; Editing by Jon Boyle and Edmund Blair)
By Tom Sims and Caroline Copley