Positive targets from overseas helped the Dax to pass the 14,000 point mark on Tuesday in quiet trading after Christmas and under thin stock market turnover.
Significant further corona easing in China provided a boost.
In the first few minutes, the leading German index rose by almost 1 percent to just over 14,000 points.
The M-Dax of medium-sized companies rose slightly less to 25,500 points.
The Eurozone leading index EuroStoxx 50 gained almost 1 percent to 3850 points.
After the most important American stock exchanges managed to shake off their opening losses on Friday and closed with profits, the mood on the stock exchanges in Asia is also positive.
China announced an end to the quarantine requirement for travelers to the People's Republic.
Because of the sharp increase in the number of corona there, experts also expect that the country could be over the current pandemic phase a little earlier than previously thought.
As the National Health Commission announced on Monday, China will no longer require quarantine for incoming travelers from January 8th.
Also, the severity of the disease is downgraded as it has lost virulence and is gradually evolving into a common respiratory infection.
"Most Chinese cities could recover from the first wave of the recent coronavirus outbreak by January, faster than expected," said Chaoping Zhu, market strategist at JPMorgan Asset Management.
While there are fears that the outbreak could be longer and weigh on the economy, developments are generally better than expected.
The Nikkei index, which comprises 225 stocks, was 0.5 percent higher at 26,543 points.
The broader Topix index rose 0.6 percent to 1,914 points.
The Shanghai stock exchange was up 0.5 percent.
The index of major companies in Shanghai and Shenzhen gained 0.8 percent.
Markets in Hong Kong and Australia remained closed on Tuesday for a public holiday.