Eda, the former chief of Japan's Science and Technology Agency, has served three terms in the upper house and four terms in the lower house.
"The makeup of the upper house has drastically changed after the upper house elections and we are facing a political situation we have never faced before," he told the session.
"I think voters' expectations for the upper house are now extremely high"
Satsuki Eda, newly elected upper house president
"I think voters' expectations for the upper house are now extremely high."
The upper house also elected Akiko Santo, a member of the LDP, as vice-president.
Abe has refused to step down despite sagging popularity and calls for his departure following a series of scandals including missing pension records and misuse of political funds.
Since he took office last September, three cabinet ministers have resigned and one committed suicide.
A cabinet reshuffle is expected later this month, according to the local media.