Deutsche Annington said the deal would create Europe's second largest real estate company after France's Unibail-Rodamco with some 350,000 flats and a portfolio totalling 21 billion euros.
Germany's residential real estate market is splintered. Around half a dozen rivals, none featuring in the blue chip DAX index of leading companies, are fighting for a slice of a huge market for rental housing.
The last big consolidation move in Germany's residential housing market was Deutsche Wohnen's 1.7 billion euro takeover of rival GSW last year, which secured Deutsche Wohnen's second-place ranking in Germany.
Annington said the combination offered economies of scale and cheaper financing costs worth about 84 million euros a year in the next two years.
"We're significantly bigger (post-merger) and we're significantly stronger on the financial side … and that means that we have a lower cost of investment," Annington Chief Executive Officer Rolf Buch said on a conference call.
Those benefits may force rivals to consider similar moves and prompt more takeover activity.
"The planned merger of Deutsche Annington and Gagfah could put significant pressure on peers to consolidate, given the significant difference in size," wrote analyst Thomas Neuhold at brokerage Kepler.
Analyst Kai Klose at Berenberg bank predicted Annington's offer would succeed given that the bidder only required a 50 percent acceptance level.
Annington will offer Gagfah investors five new Annington shares and 122.52 euros in cash for every 14 Gagfah shares.
That values Gagfah at 18 euros per share, a premium of about 16 percent over Friday's closing price and, according to Berenberg, an 18 percent premium to Gagfah's price to net asset value (P/NAV).
Gagfah shares rose 12.5 percent and Annington fell 3.5 percent by 1125 GMT.
German real estate prices rose 10 percent in the five years to 2013, twice as much as in the four years up to 2009, according to the International Real Estate Business School at the University of Regensburg.
That increase was much higher in cities like Hamburg, Berlin or Frankfurt am Main, fuelling concerns about a price bubble.
Deutsche Bank's asset management arm, however, dismissed bubble speculation saying German real estate was still relatively moderately valued on an international comparison.
(Reporting by Maria Sheahan and Thomas Atkins; Editing by Keith Weir)