Diebold has offered for every Wincor Nixdorf share 38.98 euros in cash and 0.434 of a common Diebold share.
Both companies said on October 17 they had entered exclusive talks. Based on Diebold's share price before that announcement, the offer represents an implied value of 52.50 euros per Wincor share, a premium of about 35 percent.
Including debt, the offer values Wincor Nixdorf at 1.7 billion euros, or $1.8 billion.
Wincor Nixdorf shares were indicated to open 11.3 percent higher, according to pre-market data at broker Lang & Schwarz.
A combination of Wincor Nixdorf and Diebold would lead to a global market leader in automated teller machines, with a market share of about 35 percent, leaving NCR, the global number two, with an estimated share of 25 percent, analysts have said.
The deal which is expected to yield at least $160 million in annual costs savings, will be subject to an acceptance rate of at least 67.6 percent of all Wincor shares.
Wincor Nixdorf has been looking for ways to secure its future as it suffers a weak retail banking market in Germany, deteriorating business in Russia and China, a sluggish recovery in European investment spending and falling prices for ATMs.
Its operating profit (EBITA) dropped 86 percent to 22 million euros in its 2014/15 financial year which ended in September as it restructured its business and cut jobs, and it paid no dividend for the year.