GM last made a profit in Europe in 1999.
"We have an agreement. Opel will cut 10,000 jobs in Germany. General Motors will cut 12,000 jobs overall in Europe," a GM spokesman said.
He said GM would try to prevent forced layoffs, but it would only be clear in a few months whether this would be possible.
"We have not decided on any plant closures at this time," he added. "The intent is to avoid plant closures, but there is no guarantee."
In Germany, GM will reduce headcount via state-subsidised "transfer companies" that retrain staff, early retirement, severance packages worth up to €200,000 (£138,189), and finding joint venture partners or buyers for some businesses.
Around 2,500 staff had already agreed to take early retirement offered to those born in 1946 or earlier, Opel said.
15% of managers in Europe will go in the reshuffle.
GM employed around 63,000 people at 11 production and assembly plants in Europe at the end of 2003 and produces around 1.9m vehicles a year. It has 32,000 workers in Germany.
About 2,000 jobs will be cut at GM's plants in Antwerp, Belgium; Zaragoza, Spain; Trollhattan, Sweden; and Ellesmere Port, Britain. Talks there are still going on.