The result represented a slide of five percent from the 2009 figure of €2.56 billion but was in line with an average analyst forecast of €2.46 billion compiled by Dow Jones Newswires.
Shares in the re-insurance group showed a slight gain in early trading.
Total losses from natural catastrophes last year amounted to roughly €1.56 billion, more than seven times the 2009 figure of €200 million, a statement said.
"Despite weighty major losses, which also affected us at the end of the year, we are presenting a good result," finance director Joerg Schneider said. "Our shareholders are to benefit without delay."
Munich Re's board will recommend an increased dividend of €6.25 per share, up from with €5.75 in 2009, he said.
The group also planned to buy back shares worth €500 million before its annual general meeting in 2012, the statement said.
Gross premiums written by the group last year gained almost 10 percent to €45.5 billion.
But the world's biggest re-insurance company in terms of gross premiums was hit like its rivals by a series of natural disasters in 2010, the largest of which for Munich Re was "the devastating earthquake in Chile," it said.
An earthquake in New Zealand and flooding in northeastern Australia lead to respective claims of €340 million and €270 million. Looking ahead, Munich Re said only that in 2011, it "expects a somewhat better technical result than in 2010 and a consolidated result of around the same level."
Digging into the data, Munich Re's income from investments showed a gain of almost 10 percent last year to €8.6 billion.
And the ERGO insurance group, in which Munich Re has concentrated its primary insurance activities, reported a profit of €355 million, more than double the 2009 figure of €173 million.
Shares in the group edged 0.13 percent higher to €117.50 in opening trading on the Frankfurt stock exchange, while the DAX index of German blue-chips was flat overall.